0:00 / ??? ROCK-A-BYE BABY (sway) From the recording Baby Connections Song Time $1.29 In cart Not available Out of stock Share 9. ROCK-A-BYE BABY (Sway) With Infants: The adult should hold the baby and sway from side to side. With Toddlers: Toddlers should sway from side to side, sit down and pretend to sleep.