You can't. It's really not your place, regardless of intention. I get that you feel it would be somehow kind, it very rarely would be received that way.
My sexuality is my business. Yours is yours. This is the same for all people. If you are not involved with a person sexually (like a partner) then you really have no basis to infer or ask someone else about theirs.
Here is a perfect example of how you handle it. I have a friend. For years I suspected she was a lesbian despite dating men openly, etc. She eventually told me she was in fact a lesbian. Then she spent about 5 years with one woman, they broke up, she dated a man, they married and had kids. She then divorced and started dating women again. She still occasionally dates a man. I have never once asked her. I would guess she is bisexual, but frankly why would I ask? It really doesn't matter. She is my friend. As such, we aren't sexually involved, so who she dates has no bearing on anything as long as she is happy.
If someone wants to come out to you or anyone else, they will. If they do not, then perhaps they have nothing to come out about, or are not ready, or any other reason. Sexual preferences though have no bearing on you when they do not specifically involve you. I would like to know the sexual preferences of my husband (and I think I do as far as I know) but as far as any other person on this planet, I don't care. They can tell me if they want to or not if they don't.
What you can do is be openly supportive of people who want to come out. You can make it obvious you love all people without any reservations about their sexuality so that you can feel like a safe person to talk to if someone wants to talk about it. You may very well be right about your cousin, but even if you are, if he isn't in a place to be ready, it won't help anything most likely. I made the mistake one time with someone I was very close to. I was right, but it didn't help. It ruined the relationship. I had no right to ask and in hindsight I see that now. I thought I could "help them" and all I did was make them feel unsafe. It was the total opposite of my intention.
It probably bears mentioning that both of my grown daughters have dated women. I don't know if they consider themselves bisexual, experimenting, lesbian. I don't think they consider themselves lesbian as both are in long term relationships with men at this time. But again, I don't ask them. They have told me who they are seeing, but I've never felt a need to discuss that person's gender. It makes no difference to me who they love. I only care they are treated well. I would step up and intercede if I felt they were being badly treated, otherwise I stay out of it. What is a little odd is that this is such a non issue to me, I didn't even initially have this example come to mind when answering, hence my add on. What came to mind was my first experiences in dealing with this, likely due to my first example of handling it wrongly and my next experience where I learned from that mistake & did better.