From their Website-
"Wear what you want. Dress according to your mood. It is your vacation. “Resort casual” attire is as dressy as you’ll ever have to get for dinner. But if it’s elegance you’re dreaming of, we invite you to indulge. Many of our restaurants offer formal options. If you prefer more casual dress, that’s fine, too. How you dress is up to you."
I would consider "dress shorts" (not cut-offs) as resort casual for young boys. Especially if they have a collared shirt to go with them. If you want to go to the formal night resturants on formal night, they would need at least casual slacks. Tie is optional for kids, but it woul dbe nice)
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013