bring the kids! Celebrity will accommodate them in every way possible. In fact, the waiters almost seem to thrive on the challenge, and love their innocence. Even though the children are not given a special menu, they'll be offered grilled cheese sandwiches, pizza, mac&cheese, chicken noddle soup, etc. Or they'll be offered an adult entree they can just try, with no repercussions if they take a bite and change their minds.
In fact, while my wife and I were at the specialty restaurant one evening, my kids (7/11) even had friends over at "their" table for the evening. Waiters and kids alike all had a grand ole time playing grown up. Wow.
If all else fails, they'll have the soup appetizer and ice cream for dessert. And you can hit the buffet on the way back to the room, or have them order room service (always a hit!) before they turn in the for the night.
In the end, they'll survive just fine and love being treated like an adult in the dining room.
The dining room is also a great place to teach them some basic table manners.