My Grandad used to sing this to my and my brothers and sisters (he died in Manchester, England in 1972). He lived in England all of his life and as far as I know, all our ancestors came from the UK. How on earth he came to know this song is beyond me but here is the version I know:

Go to sleep my baby
Close your pretty eyes
Angels are above you
Peeping at you from the starry skies
Great big moon is shinin
Stars begin to peep
Its time for little picaninnies to go to sleep

I still reside in England and sign it to my children but having researched it a bit I gather the word picanninie (apologies for the spelling) is a derogatory term. I always thought it just meant "baby".