Place me firmly in the "possum" variant camp. I sang this song in Junior High School in Indianapolis during the mid 1960's. It was included in a standard issue student song book.
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Oh Mister Moon, moon, bright and silvery moon,
won't you please shine down on me!
Oh Mister Moon, moon bright and silvery moon,
hiding behind that tree.
I'm gonna shoot that possum with my big shotgun,
I'm gonna shoot that possum 'fore he starts to run.
Oh Mister Moon, moon, bright and silvery moon
Oh won't you please shine down on, please shine down on,
won't you please shine down on me?