It's not in "Singing Family," Sandy, but it is in Jean Ritchie's Folk Songs of the Southern Appalachians, which I think is still in print. Jean says the song was copyrighted in 1939 by Lynn Rorhbough. Jean says her mother and father used to sing and play this party game when they were courting. I'll send Jean a personal message and ask what she can post about the song.
-Joe Offer-