Let him know that it greatly helped you, or would have, to have someone to talk to. You might go the extra step and say that you are willing to talk if he ever wants to that you will not judge him.
If would like to probe first, ouyou could tiptoe (ask him if you can ask a private question) Or you could try a semi-serious, half-joking, half-curious approach, and see if he reacts somewhat positively.
Though, In my experience, people generally tend to back off when asked about their sexuality, if they are being private about it, so I don't think you will have any success. However if you really want to ask then I tried to offer a few options that might unsettle him as little as possible. Someone else might have a better idea, though!
My recommendation on the matter is mostly "developing your friendship and being available for whenever (and if) he is ready to talk about it" approach, proposed in another post.
As a straight man, I find it sometimes bothersome, even infuriating when a gay man marries a woman and is not honest with her about his sexuality. However, I understand that gay men can marry and have relationships with the opposite sex, and, although I'm all for honesty and transparency, it's not for me to judge.
Finally, since your cousin probably knows that you came out not so long ago, he will probably already know that he can come and talk to you about homosexual matters, so there might not much need to push the topic upon him, if you have made yourself available.