Children under age four must ride in a federally approved car seat. Effective November 24, 2009, New York State law requires that children ride in an appropriate car seat or booster seat until they reach their 8th birthday.
Children under age 16 are required to wear a seat belt. The state further recommends, but does not require, that children remain in a booster seat until they reach 4'9" or 100 lbs and can sit in the adult seat belt properly.
New York's occupant protection laws are "primary enforcement" laws. That means you can be pulled over and get a ticket just for not wearing a seatbelt, or for not properly restraining your child.