Definitely. I would stick to Oasis, Quantum, Freedom or Voyager class (many going through refurbishments adding slides, trampoline, laser tag) vs older/smaller ships, but super kid friendly. We've taken our kids on Allure and Mariner (with Symphony, Navigator-post refurb, and Anthem booked) and our kids absolutely loved Allure and Mariner. We really had a great family vacation....saw many shows, participated in activities, swam, saw movies, rockwall, zipline, flowrider, and things mentioned above in refurbishment. There is also a kids menu in the MDR and even at the specialty restaurants. Our kids didn't even go to the kids club, but we got the compass and looks like they have fun activities going on as well.
Any specific ship you're looking at? How old are your kids?