Not sure what age your kids are but here are some things I learned from our last cruise with our kids 6 & 8.
Bring along some "ight lights" for cabin and cabin bathroom. The bathroom lights tend to be really bright and sometimes have a lip at the door which the kids trip over at night!
Bring some decorations from the dollar store to decorate a horse on a stick. The cruise ships usually have events where you can become the horse owner and you get to keep the horse all week and take it everywhere with you. Maybe a hula skirt or lei's or something to do with your state.
Purchase some snorkel gear at Walmart before you leave. You can get snorkel and masks and bag for $15.
Take short excursions in the morning, come back to the ship for lunch at the buffet and then shop or explore at the docked ports in the afternoon. Doing it this way you get off the ship early as you have an early excursion and have more time in the ports.
Bring along "fanny packs" for the kids so they have a place to put a bottle of water and fruit or snacks so you don't have to waste time looking for places to eat.
Hope these ideas help.
I will be sailing on January 30th with 6 of my family on the Radiance of the Seas.
Carnival Elation March 11
Carnival Imagination Sept 07
Carniival Sensation Dec 06
RCI Sovereign of the Seas Sept 06
Carnival Miracle Sept 05
Carnival Glory Sept 04
Carnival Fantasy Jan 04