My granddad sang it this way to my mom who sang it to me:

Hushabye, my baby. Slumber time is coming soon.
Rest your head on mama's breast while mama hums a tune.
The sandman is coming. The people are humming, so hushabye;
(Here they couldn't remember or were censoring the lyrics, so they hummed for 2 phrases)
The banjos are strumming, the people are humming, so hushabye.

I remember seeing it in a Reader's Digest songbook collection. My mom-in-law sings the censored line, something about "When I was a pick-a-ninny on my mama's knee"

(For those outside the US, a pickaninny is a term no longer in use for a child of African American heritage. Not complimentary!)