This is not something that needs a ton of discussion, IMO, but to sum it up.
1. The cousin was (slightly) out of line asking you the question, but if you were both drinking and having fun, I know that women (ok, and men too) often say those sorts of things when they are comfortable with someone (such as his female cousin must have been comfortable with you).
2. I don't really know why you even brought this up with your BF. But you did, and he told you that you were overreacting to her comment (which I think is probably true). Is this somewhat of a sore spot with your BF, because he probably has some issues of his own with the physical attraction he once felt with his cousin? Yes. But don't rub his nose in it. He has dealt with it, and not acted on it, so let it be.
3. I don't really know why your BF even mentioned that he once had an attraction for his cousin (as thousands of people have at one point or another in their lives, but did not act on). Think about it, how many people, over a few or quite a few drinks with their cousin, have said something like, "ya know, if you weren't my cousin...", felt a little awkward after saying that, and then just dropped it. It's normal, but most people do not act on that, as their actions are put in check by society's taboo on that sort of thing. Also remember, that for some reason he chose to share those feelings he once had with you, probably because he trusts you, knows he did nothing wrong, and wants to be open with you because he loves and cares about you.
4. He didn't act on it, so what is the big deal? People will sometimes be physically attracted to other attractive people of the opposite sex, even if those people are not people who society deems that they should hook up with. He followed society's conventions, did not act on that feeling, and moved on. He has shown no signs of wanting to act on it, and has told you that he walked away from that possibility a very long time ago.
5. You can be sure nothing happened between he and his cousin, because if it had, his cousin would not be asking YOU if he was good in bed or not (she would already know that).
MANY people need therapy or counseling to deal with issues in their relationships. You and your boyfriend, are not among those people - at least not based on this issue. Enjoy his company, don't overreact, and rest comfortably (if you really care), in the knowledge that in the distant past, he did not do the cousin.
You can't blame a man (or a woman, for that matter) for having feelings in the past before you were together, only for what he did or did not act on (and even then, unless it is something really depraved, it is usually better to leave it in the past if that is where it truly is). In this case, your man did the thing which society deems appropriate and did not sleep with his cousin. If he had, then you would have to ask yourself if that was something you seriously cared about if it was in the past, and if you did care, if it was something you could get over or not (and as a side note, it is legal in about half of the US states to marry your first cousin, even though it would not be something that I, or most people, and clearly not your BF either, would choose to do). Lucky for you, he didn't, so don't worry about it.
DO however, ask yourself if there are other things about him, that may not be exactly what you are looking for in a potential husband. If you latched onto something this minor as a reason to not get engaged, and possibly seek therapy, you may want to think about what else about him is not exactly what you are looking for, before taking the plunge.