My mum used to sing Curly-headed Baby to me when I was sick and couldn't sleep as a child, and to my boys when they were little before she passed away in 1991.

She also used to sing another lullaby but I don't know the name of the song. It had very politically incorrect lyrics that went something like:

Little Piccaninny in your cosy bed of bark
Mama lubra watches by
While the stars are in the sky
See the sun is setting o'er the mountains in the west.
Soon the sunshine you will see
Little aborigine.

I havent heard the lyrics for 40 years so not 100% certain of them.