May I recommend, for those who do not know it, a wonderful book called "Lullabies and Night Songs" which contains 48 traditional verses set to music or arranged by Alec Wilder and illustrated by Maurice Sendak. [Published by Harper [US] in 1965; The Bodley Head [UK] in 1969] -- public libraries should have copies still as I'm not sure whether it's available now.

Our family copy is well-worn and was much used as we sat around the piano playing and singing (the accompaniments are not difficult). Do families still do this? My middle son (born 1969) brought his partner to visit recently and specifically asked to hear many of his favourites again.