I understand your frustration. I'm in the same predicament. Think of St. Monica who was St. Augustin's mother and how many years she had to pray for his conversion! Take consolation in knowing that even the saints had to wait sometimes. You might want to consider praying to her to intercede for you with God.
The greatest thing you can do is have Masses said for their conversion. This is what I've learned from books on Theology, the writings of the saints, and my Catholic education before Vatican II. There is nothing better to offer to God the Father than the sufferings and death of His Son, which is what happens in the Mass.
Next to that you can make the novena to the Sacred Heart which Padre Pio made. It is available on the Internet. I've made it and have received graces from doing so. You can make the devotion of the First Fridays to which Jesus has attached many promises.
The prayers of Our Lady come next as being the most powerful with God, for She is without sin and is the closest of all God's creatures to God Himself (a creature being defined as someone who is not God). Her prayers are most efficacious. The Rosary takes first place. You can also say the Litany to Her to ask Her to intercede with God for this grace. Also there is the Memorare which I think St. Bernard composed and it's very efficacious as well for obtaining graces.
As for the saints, St. Joseph, of course, is powerful. There is a litany to him. Then there are Saints Jude and Rita who are known to be able to obtain graces from God for even "impossible" cases. I believe the prayers to St. Jude require that you make known publicly that your prayer was answered, which you could do here on this forum.
There is the Litany of All Saints where you call on the most powerful and well-known saints in heaven asking them to intercede for you for your intentions.
You could pray to the patron saint of each person to ask for their conversion.
You could pray to the guardian angel of each person asking them to help that person be receptive to God's inspirations to amend their lives and help defend them from evil inclinations.
The key factor is that you have FAITH in God that He CAN give such a grace and CONFIDENCE that the grace will be given if God so wills. And you must be willing to accept the fact that this grace or any grace for which you ask will be given when GOD thinks it best, which may not be when YOU think it best. So perhaps God has agreed to answer your request but the conversions will take place only on their deathbeds. This info is right from the books on Theology and the writings of the saints.
You can also do other things such as practice mortifications and penances to go along with your prayers. Christ said in the Gospels that some graces can only be obtained by "prayer and fasting."
You can offer up all you do, every single thing you do that tends to the glory of God -- which is everything that is in line with the Commandments and the Evangelical Counsels of the Gospels -- and ask Jesus to unite your works with His when He was on this earth and He can offer them to God the Father for your intentions. This is getting a little deeper into theology but again, it is recommended by the saints. It has to do with us being members of the Mystical Body of Christ--spiritually we are united to Him by being in the state of grace and so we can use His merits to offer to God the Father for our requests. You can also offer up His sufferings during His Passion for your intentions. This is NOT the same as what the priest does at Mass. You can find explanations of this in books written for nuns and priests before Vatican II. That is what nuns used to do every day for the salvation and conversion of sinners, especially the cloistered nuns. Prayer and penance for the salvation of souls and the good of the Church was their daily work, but this was not exclusively for nuns to do! It's just that nuns devoted their time to it, as they had no obligations to family or a secular job, etc., which would prevent them from spending their lives this way. Also, they had consecrated their virginity to God forever, which made them closer to God than non-consecrated people provided they lived what they professed to do.
Our Faith is very rich with many, many devotions that have been used through the ages to obtain graces from God. Unfortunately, since the Council devotion to the Mother of God and the saints has been de-emphasized because the new teachings say that everyone is okay, God is all-forgiving and we need not worry about His Justice and punishment for sin, no one needs to be converted, etc. The old prayer books and instructional manuals have been thrown out or burned because they contradict this teaching, and those who were born and raised after Vatican II have little to no idea about these things and what treasures we had before the Council and how often people used these practices to obtain graces. So your question is a very legitimate one.
But don't even start to feel overwhelmed by what I've written. I'm just giving you suggestions. What God looks for is a sincere heart and FAITH that He CAN do what you ask and that He WILL do what you ask provided He thinks it best. And oftentimes He puts the desire into someone to make such a request as you are making so that He can give the desired grace. He doesn't want people to go to hell. He commands us to love our neighbor as we love ourselves. We pray for our own salvation. We should pray for the same for everyone, especially those whom He has placed in our life.
There is no "magic prayer" as some may think. But some prayers are more pleasing to God than others because of the person making them because those people are closer to God in holiness than we are and/or the prayers themselves contain more proper sentiments than we on our own may not express, such as an acknowledgement of our belief that He is powerful and good enough to listen to us and help us, that we are sinners and depend on Him for every good, etc.
An example of Someone Whom God loves greatly and always listens to is Our Lady for She is without sin; She was not conceived in Original Sin nor did She ever use Her free will to sin. She spent Her entire life only for the glory of God and doing His Will perfectly, so She has a very high place in heaven.
But God never turns away from a sincere heart asking with true Faith for help even if we forget to mention all the points that are contained in some formal prayers. Witness the incidents in the Gospels where the centurion asked for help for his daughter and his faith was so strong that he told Jesus that He didn't even need to come to his home to see the girl, that he believed that all Jesus had to do was will for her to be healed and she would be--and she was. Consider the woman who believed if she just touched the hem of His garment her hemorrhage would stop. It did. FAITH. God looks for FAITH.
If you want specific prayers or litanies, let me know. You can PM me. I have many books to draw from and I just ordered a book of 200 litanies from before Vatican II. I'd be glad to share with anyone. I try to find things that were written before Vatican II in their original form and not reprints of the same thing which may have been edited to be more "correct" according to today's understanding.
I hope you live to see your prayers answered. At least know that God is pleased with your requesting this grace. You will gain merit for doing so which will matter when you are judged and go towards your reward in eternity, according to the saints.