The best snowpack this spring is in the northern mountains of Colorado. Therefore, the best and, possibly, longest runoff period will be on the upper Colorado and Arkansas Rivers. So, the Browns Canyon portion of the Arkansas (Buena Vista-Salida) may still have ok rafting in August. The San Juans have had very poor snow, so the Animas, La Plata, Navajo, San Miguel, Dolores, and San Juan Rivers will likely be very low except just below Navajo and McPhee Dams.
Depending on whether you have been rafting in Colorado before, the type of rafting you want to do (Class II or Class IV?), and the importance of getting to southern Utah, you might try a trip through Ruby-Horsethief or Westwater Canyons near Grand Junction. It is on the Colorado River, so may still have water in August. But check
HERE for information on available raft trips and again before you leave just in case there is no water in the river.
Those who keep saying August is HOT in Moab know whereof they speak. Field mapping in the Moab-Arches-Canyonlands area in June while living in a tent (with no shower for a week) was bad enough, but August is worse! Always carry plenty of water, especially if you have kids with you, as some of the public campgrounds ration the amount of water they can provide (water has to be trucked into some campgrounds).