From The Catholic Encyclopedia 

Substitutes for the sacrament
The Fathers and theologians frequently divide baptism into three kinds: the baptism of water (aquæ or fluminis), the baptism of desire (flaminis), and the baptism of blood (sanguinis). However, only the first is a real sacrament. The latter two are denominated baptism only analogically, inasmuch as they supply the principal effect of baptism, namely, the grace which remits sins. It is the teaching of the Catholic Church that when the baptism of water becomes a physical or moral impossibility, eternal life may be obtained by the baptism of desire or the baptism of blood.
The baptism of desire
The baptism of desire (baptismus flaminis) is a perfect contrition of heart, and every act of perfect charity or pure love of God which contains, at least implicitly, a desire (votum) of baptism. The Latin word flamen is used because Flamen is a name for the Holy Ghost, Whose special office it is to move the heart to love God and to conceive penitence for sin. The "baptism of the Holy Ghost" is a term employed in the third century by the anonymous author of the book "De Rebaptismate". The efficacy of this baptism of desire to supply the place of the baptism of water, as to its principal effect, is proved from the words of Christ. After He had declared the necessity of baptism (John 3), He promised justifying grace for acts of charity or perfect contrition (John 14): "He that loveth Me, shall be loved of my Father: and I will love him and will manifest myself to him." And again: "If any one love me, he will keep my word, and my Father will love him, and we will come to him, and will make our abode with him." Since these texts declare that justifying grace is bestowed on account of acts of perfect charity or contrition, it is evident that these acts supply the place of baptism as to its principal effect, the remission of sins. This doctrine is set forth clearly by the Council of Trent. In the fourteenth session (cap. iv) the council teaches that contrition is sometimes perfected by charity, and reconciles man to God, before the Sacrament of Penance is received. In the fourth chapter of the sixth session, in speaking of the necessity of baptism, it says that men can not obtain original justice "except by the washing of regeneration or its desire" (voto). The same doctrine is taught by Pope Innocent III (cap. Debitum, iv, De Bapt.), and the contrary propositions are condemned by Popes Pius V and Gregory XII, in proscribing the 31st and 33rd propositions of Baius.
We have already alluded to the funeral oration pronounced by St. Ambrose over the Emperor Valentinian II, a catechumen. The doctrine of the baptism of desire is here clearly set forth. St. Ambrose asks: "Did he not obtain the grace which he desired? Did he not obtain what he asked for? Certainly he obtained it because he asked for it." St. Augustine (On Baptism, Against the Donatists, IV.22) and St. Bernard (Ep. lxxvii, ad H. de S. Victore) likewise discourse in the same sense concerning the baptism of desire. If it be said that this doctrine contradicts the universal law of baptism made by Christ (John 3), the answer is that the lawgiver has made an exception (John 14) in favor of those who have the baptism of desire. Neither would it be a consequence of this doctrine that a person justified by the baptism of desire would thereby be dispensed from seeking after the baptism of water when the latter became a possibility. For, as has already been explained the baptismus flaminis contains the votum of receiving the baptismus aquæ. It is true that some of the Fathers of the Church arraign severely those who content themselves with the desire of receiving the sacrament of regeneration, but they are speaking of catechumens who of their own accord delay the reception of baptism from unpraiseworthy motives. Finally, it is to be noted that only adults are capable of receiving the baptism of desire.

The baptism of blood
The baptism of blood (baptismus sanquinis) is the obtaining of the grace of justification by suffering martyrdom for the faith of Christ. The term "washing of blood" (lavacrum sanguinis) is used by Tertullian (On Baptism 16) to distinguish this species of regeneration from the "washing of water" (lavacrum aquæ). "We have a second washing", he says "which is one and the same [with the first], namely the washing of blood." St. Cyprian (Epistle 73) speaks of "the most glorious and greatest baptism of blood" (sanguinis baptismus). St. Augustine (City of God 13.7) says: "When any die for the confession of Christ without having received the washing of regeneration, it avails as much for the remission of their sins as if they had been washed in the sacred font of baptism."
The Church grounds her belief in the efficacy of the baptism of blood on the fact that Christ makes a general statement of the saving power of martyrdom in the tenth chapter of St. Matthew: "Every one therefore that shall confess me before men, I will also confess him before my Father who is in heaven" (verse 32); and: "He that shall lose his life for me shall find it" (verse 39). It is pointed out that these texts are so broadly worded as to include even infants, especially the latter text. That the former text also applies to them, has been constantly maintained by the Fathers, who declare that if infants can not confess Christ with the mouth, they can by act. Tertullian (Against the Valentinians 2) speaks of the infants slaughtered by Herod as martyrs, and this has been the constant teaching of the Church.
Another evidence of the mind of the Church as to the efficacy of the baptism of blood is found in the fact that she never prays for martyrs. Her opinion is well voiced by St. Augustine (Tractate 74 on the Gospel of John): "He does an injury to a martyr who prays for him." This shows that martyrdom is believed to remit all sin and all punishment due to sin. Later theologians commonly maintain that the baptism of blood justifies adult martyrs independently of an act of charity or perfect contrition, and, as it were, ex opere operato, though, of course, they must have attrition for past sins. The reason is that if perfect charity, or contrition, were required in martyrdom, the distinction between the baptism of blood and the baptism of desire would be a useless one. Moreover, as it must be conceded that infant martyrs are justified without an act of charity, of which they are incapable, there is no solid reason for denying the same privilege to adults. (Cf. Francisco Suárez, De Bapt., disp. xxxix.)

St Alphonsus is perfectly in line with Trent. BoD is not a sacrament but just analogically so as it lacks matter and form. If St Alphonsus was in error in his teaching on BoD, he would have been condemned but instead was canonised by Gregory XVI and later proclaimed doctor of the Church by Pius IX.

So when you are presented with St. Alphonsus seemingly being in error regarding the effects of BOD while attempting to define it (one of the same BOD definitions BODers use to support their arguments)...all you have to say is.."St. Alphonsus was correct. If he was incorrect, he would have been condemned".

Was St. Alphonsus infallible? Was every single thing he ever wrote canonized with him? Do you believe there is any chance at all that there can be an error in a Church Fathers or Doctors writings?
Are you really so obstinate that you cannot even acknowledge the apparent contradiction as it's staring you in the face?

St. Alphonsus:

Baptism of desire is perfect conversion to God by contrition or love of God above all things accompanied by an explicit or implicit desire for true baptism of water, the place of which it takes as to the remission of guilt, but not as to the impression of the [baptismal] character or as to the removal of all debt of punishment.

TRENT:

For, in those who are born again, there is nothing that God hates; because, there is no condemnation to those who are truly buried together with Christ by baptism into death; who walk not according to the flesh, but, putting off the old man, and putting on the new who is created according to God, are made innocent, immaculate, pure, guiltless, and beloved of God, heirs indeed of God, but joint heirs with Christ; in such a manner that absolutely nothing may delay them from entry into heaven

But though He died for all, yet all do not receive the benefit of His death, but those only to whom the merit of His passion is communicated; because as truly as men would not be born unjust, if they were not born through propagation of the seed of Adam, since by that propagation they contract through him, when they are conceived, injustice as their own, so unless they were born again in Christ they would never be justified, since by that new birth through the merit of His passion the grace by which they become just is bestowed upon them.”

If there is no contradiction here, explain it.

Explain how "debt of punishment''" remaining conforms with "absolutely nothing may delay them from entry into heaven"

Explain how "debt of punishment"="absolutely nothing"

Now ... a strictly limited BoD such as what St. Robert held, would not create fatal damage to Catholic ecclesiology, where it's only possible for Catechumens and those who are practically such, with explicit faith in the Holy Trinity and Incarnation, and intending to become Catholic (even if their status had not been formalized).

Correct.  The BOD of St Thomas/St Robert, for CATECHUMENS, is not heresy.

But the SECOND you extend BoD to anyone else, to infidels, for instance, or to heretics (and it's laughable, and exposes their motivation when some apply BoD to even baptized Protestants), but once you extend the possibility of salvation to non-Catholics ... YOU HAVEN'T GOT A LEG TO STAND ON IN OPPOSING VATICAN II.

BOD for non-catechumens (i.e. those who are still in, accepting, practicing non-catholic religions) is heresy.

So when you are presented with St. Alphonsus seemingly being in error regarding the effects of BOD while attempting to define it (one of the same BOD definitions BODers use to support their arguments)...all you have to say is.."St. Alphonsus was correct. If he was incorrect, he would have been condemned".

Was St. Alphonsus infallible? Was every single thing he ever wrote canonized with him? Do you believe there is any chance at all that there can be an error in a Church Fathers or Doctors writings?
Are you really so obstinate that you cannot even acknowledge the apparent contradiction as it's staring you in the face?

St. Alphonsus:


TRENT:


If there is no contradiction here, explain it.

Explain how "debt of punishment''" remaining conforms with "absolutely nothing may delay them from entry into heaven"

Explain how "debt of punishment"="absolutely nothing"

Here you go putting sacramantal Baptism and BoD into the same boat. When St Alphonsus says that the guilt of original sin is removed by BoD and not the temporal punishment due he is talking explicitly about BoD. Unlike sacramental Baptism or Baptism with water which remits the guilt of original sin and any temporal punishment due. 

Here you go putting sacramantal Baptism and BoD into the same boat. When St Alphonsus says that the guilt of original sin is removed by BoD and not the temporal punishment due he is talking explicitly about BoD. Unlike sacramental Baptism or Baptism with water which remits the guilt of original sin and any temporal punishment due.

You're incredibly dense, aren't you?  It's been splained to you multiple times.  If you don't get it by now, then you need to just drop off the thread, pursue additional education, and perhaps come back in a few years.

We're saying that what "St. Alphonsus says ..." contradicts the Council of Trent, not disputing what he says.

I'll give you one more chance to follow closely.  Trent is making no distinction between Baptism or BoD or any of the concepts that you hopelessly conflate.

TRENT SPEAKS OF INITIAL JUSTIFICATION in those passages, as you BoDers who constantly (and mindlessly) regurgitate this passage should know.  It's not talking about Baptism OR BoD per se, but about JUSTIFICATION.  You BoDers claim that JUSTIFICATION can happen by the Sacrament OR ELSE by the Desire.  So those are just means of obtaining JUSTIFICATION, per your own reasoning, so I'm not sure I understand your befuddlement.

TRENT TEACHES THAT JUSTIFICATION REQUIRES REBIRTH.
TRENT THEN DEFINES REBIRTH AS A COMPLETE RENEWAL SUCH THAT NOTHING REMAINS THAT COULD EVEN DELAY ENTRY INTO HEAVEN.

Consequently, TRENT CLEARLY TEACHES THAT IN ORDER FOR THERE TO BE THAT INITIAL JUSTIFICATION, THERE MUST BE A REBIRTH, IN SUCH A WAY THAT THERE CAN AFTER SAID INITIAL JUSTIFICATION BE NOTHING LEFT WHICH DELAYS IMMEDIATE ENTRY INTO THE KINGDOM OF HEAVEN.

It's so simpley that a child could follow it, or anyone without a heretically-depraved mind.

So that would mean you can't be justified by justification of desire?

No.  This merely says that there's nothing left to ACTIVELY STOP or PREVENT or ... DELAY (key word as to why it undermines St. Alphonsus' theory about the temporal punishment to sin) entry into the Kingdom.

But it doesn't mean everything necessary is PRESENT.

In other words, you're not barred from entry into the Kingdom of Heaven by sin or any kind of enmity with God ... but you also don't have the requisite Baptismal Character in order to enter the Kingdom either.

It's the difference between lacking something and having something that would prevent you from entering.

You can have that Baptismal character, but be barred from Heaven (by being in a state of mortal sin).

But you can not be in a state of sin (not being barred), but simply don't have the necessary Wedding Garment, so to speak, to enter.

This is one of the major problems I have with BoD.  In order to enter Heaven proper, aka to see the face of God, the Beatific Vision, we human beings simply don't have the capability, or, in scholastic terms, the necessary FACULTY in order to see God this way.  THAT is what the Character of Baptism does for us.  It instill in the souls this additional capability whereby we can see God, and also enter into the life of the Holy Trinity, where the character imprints the likeness of God the Son in our souls, thereby rendering us in a way, members of the family of the Holy Trinity ... by adoption, meaning, not by natural right, but by God's extension of this relationship to us by His positive will.

There's this quasi-Pelagian view of human nature that's prevalent among the BoD-tards, namely, that simply not being in a state of mortals sins qualifies someone for Heaven.  OK, tell that to the infants in Limbo, or to St. Joseph and St. John the Baptist before Our Lord's Ascension.  St. Joseph and St. John the Baptist were clearly in a state of justification.  Why couldn't they enter Heaven?  Now, one BoD-ite famously answered this question with ... "because Christ hadn't opened the gates of Heaven".  Meh, no, not really.  There's more of an ontological reason.  I agree with those Church Fathers, cited extensively with the Dimond Brothers, that the OT Just were raised from the Dead after Our Lord's Resurrection and then Baptized, so they coud then enter Heaven.

Entery into the Kingdom of Heaven requires a special free gift in addition to simply being in a state of justification, an ELEVATION of our human nature, which by itself is simply not capable of experiencing the Glory of Heaven.  St. Gregory nαzιanzen, in the famous passage where he rejects BoD, says that there are some who are not bad enough to be punished (aka are in a state of justification) but not good enough to be glorified (i.e. don't have the glory, the seal, aka the character of Baptism that would enable them to enter the Kingdom).

I personally believe that there are two aspects of "Heaven", where there's the Kingdom proper, which is where the adopted members of the Royal Family of the Trinity dwells, but that just outside of it you have those who died justified, who are also attached to and related to the Kingdom, but simply lack that additional election to become "insiders" within the Family of the Holy Trinity.  Then there are others like the Infants in Limbo who lack any kind of positive justification, nor do they have any reason to be punished due to actual sin, and they're in a more natural state of happiness, but falling short of what we might experience here on earth being happily in a state of grace.  Then after those are the ones who are punished to varying degrees according to the state of their souls after death, some relatively mildly, and others in unspeakable agony.  But in all cases, the degree of happiness and unhappiness that each individual experiences in eternity is of their own making ... with the exception of that fee gift of election, of being invited into the Banquet Hall, into the Kingdom, to adoption in the Royal Family of the Holy Trinity.  That is free gift, completely unmerited, and there's nothing one can do that gain that in justice (which is why it's referred to by the Fathers as glory or glorification).