Chants for babies

There are special rhymes for different games with a baby, e. g. clapping rhymes. In Russian, there's a special verse that we say when the baby sits on our knees and we do such an up-and-down movement and then pretend to drop the baby. Does anybody know rhymes like that (for playing with babies? not only making them jump on your knees) in English?
UPD: "Rockabye Baby" is one of them.