The way I did it (convert spouse) was not to actively try. It took over 10 years, but it happened and I saw it slowly unfold. I just quietly set a Catholic example of a holy Catholic life, as best I could considering how flawed I am.
First, those of the world are proud, so don't challenge or argue with the spouse, it makes them dig in more and makes it harder for them to convert. They don't want to admit you are right. Classic husband - wife drama.
Second, just be a good Catholic. Go to Mass, say your prayers before meals, say your rosary, be kind at all times, especially to your spouse! No matter how angry he/she makes you, always be kind. Always. No matter what they say or how hurt or angry you get, be kind. Offer your suffering, and move to the spouse, giving them a hug and say I love you.
Some examples of what I did
1. Going to Mass . The day before, making plans for Sunday or a holyday, "I'll be attending 8am Mass, would you like to come with me? " When it was "no", I just said, ok I'll be home around XXXX and we can have a nice breakfast together. How would you like to enjoy the rest of the day? What would you like for dinner?"
I never criticized or preached. When spouse was receptive (read the mood first!) I'd say "I pray you and I can someday share our Faith the same way" but I'd always smile and warmly hug / kiss too. I NEVER scolded or provided an opportunity for a stubborn position out of pride. The best way to conquer prideful reactions is with an abundance of love and good sense of humor.
2. Prayer before/after meals. When spouse does not participate, I'd quietly say "excuse me just one minute" then I'd offer the prayer, bless myself, and resume our meal conversation.
3. The same with rosary... before spouse conversion, we watched tv. (now we do not). I'd excuse myself very quietly "Honey, I'll be back in about xxxx minutes - I want to offer a < rosary or devotion> for our family. Can I bring you <a cup of tea> when I return?"
4. Weave in trad Catholic teaching whenever you can, but not as a catechism instruction unless specifically asked. My spouse started to ask direct questions, and that's when I would also be direct. Otherwise, it must be casual comments. Perhaps when discussing politics. Or when you are not sure about a situation say "I must look into what the Church teaches about that". Spouse learns by this that you subject yourself first and foremost to Christ.
5. Always be matter of fact, not contentious. And if your spouse is a man, be as sweet as possible, and always maintain a great sense of humor. If he is in a bad mood, just be supportive and a little playful, funny then give him space.
Spouse must see that your faith is priority, and you integrate it into your everyday life while still loving him/her. Your Catholic life becomes the family culture. Never attack or accuse or even fight back, it does not work with most people.
In the end, your salvation is what is most important. Set the example and pray and never ever give up hope. The suffering you endure now can be offered for your spouse's conversion, so every time you feel hurt or sad about it, offer it for your spouse. God has entrusted this person to your goodness and example.