Monteverde isn't really that close to any of the good boating in Costa- it's a stout drive up a long dusty road. You're not too that far from Arenal (2-3 hours), where there are a couple of Class III stretches; and the Sarapiqui (http://www.rancholeona.com/htm/kayaking.htm
) is just to the south of that region.
You'll be there long enough to plan trips to Turrialba- just walk into the Hotel Interamericano and you'll probably run into a group of paddlers in the lobby. Bring your personal gear, but buy a boat from someone getting ready to leave the country. If you stay there often enough, Blanca will let you keep your boat and gear under the hotel for a few bucks a week- that way you can take a bus from Monteverde down to Turrialba whenever you get a free couple of days, and you'll always have you stuff right near the rivers (but not have to cart it around the country). It's been six years since I've been down, so I'm sure other folks will have a lot more info than I do about shuttle drivers, contacts, places to rent stuff, etc.