Sounds like your friend is in stealth.
I don't think you have the right to tell them. Don't be a pest and wreck the relationship.
But I don't give good odds if they're keeping secrets from their significant other.
I would start by opening a discussion with the friend. If they are your friend, outing them is bad. Instead, see if you can get them to open up a bit, to tell the cousin on their own.
Your friend is probably miserable being dateless (don't force that on them). They'd be equally miserable by in the closet, probably.
Reading the later posts, it's clear that you tackled this in a very awkward and pushy way.