The Ocoee will be running and it's great III+ (IV) water. One of the best play runs in the U.S. Don't miss it if you're in the area. There are also plenty of rivers (mentioned above) that you could hit in AL.
It's never a stretch to assume that there is whitewater in the Southeastern U.S. There's tons of it and it runs when it rains (which is generally often) or when power is needed, and almost every southern state has it - TN, AL, KY, SC, NC and GA.