When I was a kid, my mother used to sing it with these lyrics. She was born in 1926. I don't recall any other verses.

Oh, Mister Moon, Moon, Great big silver moon
Quit yer hiding behind that tree
Somebody's waiting with a Gatling gun
Somebody's waiting just to have a little fun.
Oh, Mister Moon, Moon, great big silver spoon
Won't you please shine down on me?