Yes they have some sort of nursery where you can drop them off.baby sitting is available at about 10$ an hour.
How old is the baby? Group child sitting, known onboard as the "Late Night Party Zone", is available on all ships and is supervised by the youth staff. The service is offered from 10:00 PM to 1:00 AM in the youth facilities. Children must be three years of age, potty trained, and pull-up diaper free to enter the youth facilities and participate in activities. Rate is $5 per hour per child.
In room babysitting - Sitters are available between 8:00 am and 2:00 am. Sitters will be assigned on a first come first served basis. Babysitting cannot be booked prior to the cruise vacation and there is no guarantee that sitters will be available. The service is offered when personnel is available. Children MUST be at least 1 year old. Approximate Rate: $8.00 per hour