Consider the Green River in Utah between Jensen and the town of Green River. This is after the river leaves Dinosaur National Monument and before the "Labyrinth" section (which itself is above the confluence with the Colorado and subsequent Cataract Canyon). Google DesoGray (Desolation Canyon and Gray). Here is one description (happens to be for a guided trip): http://www.griffithexp.com/trips/family-rafting-green-river.htm