Cayo did some paddling in Belize. I remember the post because I've been to the lodge that is close to the river they paddled. I tried to find some info on kayaking, but it seems to be pretty poorly developed down there. There are definitely rivers to run though. It depends a lot on the timing though. I buddy went down during the rainy season and said the little creek tumbling over 5 sisters falls was a raging flooded monster.
I spend some time on caye ambergris diving, and spent some time in the mountains checking out caves, waterfalls, ruins etc. There's plenty to keep you busy down there without the boating. I'd probably skip the boating and go for the other fun stuff. If you have gear and want to go on a mission, then go for it.
Sounds like slickrock adventures has some paddling in inflatables for their "adventure vacatations". I talked to them before I went down, but it was in the dry season and nothing was running.
Very cool place, have fun.