rock-a-bye
/ˈrɒkəbʌɪ/(also rock-a-by)
exclamation
Used to soothe an infant to sleep, especially in accompaniment to the rocking of a cradle or the rocking of the infant in one's arms. Frequently in nursery rhymes, especially in rock-a-bye, baby. Also in (usually humorous ) extended use.
Origin
Early 19th century; earliest use found in Songs for Nursery. From rock + -a-, connective element + bye.