Just outside Kings Canyon National Park you'll find the Kaweah River in the town of Three Rivers, CA, about 20 minutes from the park entrance. A little further north is the Merced River, which is a short two hour drive from Sequoia - Kings Canyon.
There are several more California whitewater rafting rivers within a 4 - 6 drive from Sequoia National Park.
See a map showing all 10 of our California Rivers with more information about each: