Thanks for this! My mother used to sing a version which she said was "a minstrel song" that she'd learned at camp in the 1940's; it went:

Oh, Mr. Moon, moon, bright and shiny moon,
Won't you please shine down on me?
Oh, my life's in danger and I'm scared to run.
There's a man behind me with a big shotgun.
Oh, Mr. Moon, moon, bright and shiny moon,
won't you please shine down on --
Talk about your shine-on --
Please shine down on me.

My web-search was prompted by encountering the "round and golden sun" version; I'd wondered which came first.