There are two paddling groups here, The Bluff City Canoe Club and Memphis Whitewater. From April to September, the Memphis Whitewater group plays kayak polo on Tuesday evenings, after work at Patriot Lake. We try to make it beginner friendly, so everyone is welcome. There are also a handfull of us that do kayaking workouts at Patriot, as well. Some of the same folks paddle the Mississippi pretty regularly.
http://memphiswhitewater.com/

I dont know much about Bluff City, but you can check them out here:
http://www.bluffcitycanoeclub.org/