Hi hb mom:
I'm the family cruise editor here. I think Royal Caribbean has a better atmosphere for non-partiers and their youth program is tops. However, their youth program is for those three years and older who are potty trained. Most lines are pretty strict about making sure kids are three and older in order to participate (and the youth counselors have your DOB info, etc. so they'll know if you're lying!) Once in a while, they'll bend the rule, but often they don't.
Carnival, on the other hand, also has a very good youth program and it is for those two years and older. Counselors DO change diapers of those in the youth program.
Let me know if you have any add'l q's.
Smooth sailing,
Luisa Frey Gaynor