I was sung to sleep with "You are my Sunshine"
My daughter prefers "The Worm Song" followed by a modified "Rockabye Baby"
viz
Nobody loves me, everybody hates me, gonna go eat some worms. Big, fat slimy ones, little, smally crawly ones, pick 'em up and watch 'em squirm. Bite the head off, suck the juice out, throw the skins awaaaaaaay. No one knows how well you live on worms three times a day.
then
Rockabye, Big Girl, on the tree top When the wind blows, big girl's bed will rock When the bough breaks, big girl's bed will fall and down will come Big Girl, her bed and all.
She likes it... so do I