I remember the song going much the same way but I learned it with a slow, sweet beginning, which is probably why kids were rocked to sleep with it...

Tell me why the stars do shine
Tell me why the ivy twine
Tell me why the sky's so blue and I will tell you why I love you
Because God made the stars to shine
Because God made the ivy twine
Because God made the sky so blue and that's the reason why I love you..

Oh Mr. Moon, Moon, bright and silvery moon
Hiding behind that tree
Oh Mr. Moon, Moon, bright and silvery moon
Won't you please shine down on me?
I'm gonna shoot that possum with my big shotgun
Shoot that possum 'fore he starts to run
Oh Mr. Moon, Moon, bright and silvery moon
Won't you please shine down on
Please shine down on
Please shine down on me...shine down on me