Well, for starters, always reinforce the fact that he is obligated to honor his parents. If he has the desire to convert, but his parents won’t allow him to, God won’t hold it against him.
The advice they usually give on CAL is that he should honor his parent’s wishes on the matter, but show them how he has changed in regards to this. He should start studying the faith in depth, to show that this is not some ad hoc decision he’s making. If they aren’t willing to take him to mass, then he should ask if they would allow him to attend Bible study at the parish. He might also ask if he could attend RCIA to learn about the faith. There is no obligation attached to the classes, and no cost (except maybe to cover the cost of study materials, it depends on the parish.)
If his parents are completely against it, then he’s going to have to live with that. I know it seems like a long time right now, but it’s only three years until he’ll be able to make the decision for himself. The church will still be here in three years, and if he truly desires to convert, God knows that, and God will honor that desire, even if his parents won’t.
Above all, tell him to keep involved in the faith, even if it’s only through study. We’d love to have him on the forums here, and EWTN has a boat-load of free materials, shows, etc. that he could listen to so he can stay engaged prior to his conversion, as does Catholic Answers. One of my personal favorites programs is
Christ is the Answer.