We are good friends - we just dissagree on this issue.....and we pretty much avoid that issue
Gays can get married, and often do. What's illegal (because it contradicts the very definition of "marriage") is men marrying men, and women marrying women. It's also illegal (in our culture) for "marriages" to include young children, close relatives, non-humans, multiple persons, etc.
What your cousin should want is a civil contract that is mutually binding in the same manner as "marriage".