My daughter, when she was 12, and Max, when he was 9, started out in a Dagger Dynamo. This is a great kid's boat to start out in, but hard to find as it seems like Dagger has not marketed the boat in the US since 2002 or so. You can still buy it on the other side of the pond. Max is now almost 14, a bit small for his age, but he used the Dynamo this season when competing in Boater-X and playing kayak polo.
As Glenn pointed out, the Dagger Axiom seems to be in the mold of the RPM and Dynamo. Not sure if the smallest Axiom is small enough for young kids.
The Rebel is Pyranaha kid's boat. Max demoed the Rebel earlier this year just for kicks and he thought it was similar his Dynamo. Here is a link to the video of his session on Clear Creek in Golden, CO.
Jackson has kid sized boats for river running (Sidekick), river running playboat (Fun 1 and Fun 1.5) and freestyle (Shooting Star). Max competes in freestyle using a Shooting Star and he loves that boat.
Another option for a kids boat would be the Wavesport Fuse 35. Is a river running playboat and a used Fuse 35 can be had for a song. This was the boat that Max used when he first got into freestyle. He really like the boat, but since it is not a true freestyle boat it was not competitive with the Shooting Star. So we ended up selling the boat, the Harmony kid's skirt made for the Fuse, and a paddle for $300. I wish that kind of deal was available when my kids got into kayaking.
Liquid Logic Remix 47 is a true river runner and according to some very accomplished paddlers this is a great kid's boat. My daughter had her first combat roll in this boat when she demoed it.