Actually, my (bi) younger sister did a pretty good new lesbian song, with strong traditional style; it's set to "The Irish Sea" as performed by Clam Chowder, with new lyrics by a young woman whose best friend/lover is being forced by her father to marry a nobleman's son. It's an entirely traditional-style lament, and rather moving.

But no, I certainly don't know of any actual traditional gay folk; 's the sorta thing you didn't advertise in most of these times and places.

Of course, a lot of trad stuff is easy to adapt to the theme; just have the other gender sing it, with feeling. Heard a charming young man at a recent SF convention singing all those old favorites like Cripple Creek:

Goin' over Cripple Creek as fast as I can;
Goin' over Cripple Creek to see my man.
I'll hug him and kiss him...

--Nonie