Baby Swing Harness : Target Shop for baby swing harness online at Target. Free shipping on orders of $35+ and save 5% every day with your Target RedCard. Baby Swings : Target A rocker baby swing can be used to soothe infants and give the new parent a break. Swings, with their back and forth motion, have been known to help settle tummies and give relief from colic. At Target, find a wide range of baby swings to best suit your little one’s needs.