Not happening in the fall. You can do a lot of flat water kayaking on various lakes, and all along the lower Colorado River below Hoover Dam, Davis Dam, Parker Dam, Palo Verde Dam, Imperial Dam, Laguna Dam, etc. But I have never heard of any one going white water rafting in the fall. There just isn't enough water. The lower Colorado begins to be fun for multiday flatwater trips with good current, in the fall, because the weather gets nicer down there!
Watch the river data website and you'll see:http://waterdata.usgs.gov/az/nwis/current/?type=flow
Looking at this, I see that the Upper Salt River (Chrysotile), which has Class II to IV in the spring is now running at a disappointing 110 cfs. The lower Verde, discussed elsewhere, looks more promising, but people were saying you can't go along by the Indian reservation. The Lower Salt also looks promising, at over 900--at least you can float it at that level!
As you can see, it's only BELOW dams that these rivers have any cfs at all.
Now for the San Juan, Green, and upper Colorado Rivers, we have to go to Utah: http://waterdata.usgs.gov/ut/nwis/current/?type=flow
Looks like the Green and Colorado Rivers are happening, but the San Juan is low, at 477. I don't know if you can kayak it at that level. I kayak the lower Colorado by downtown Yuma at that level and lower, but it's pretty shallow. If you hit a sandbar, you get out and wade!
In New Mexico, the Rio Grande and Rio Chama seem to be running at very modest levels, but may be floatable: http://waterdata.usgs.gov/nm/nwis/current/?type=flow
Right now, if I wanted to do a multiday trip, I'd put in above Blythe CA, below Parker Dam, and canoe/kayak to Squaw Lake CA, or Martinez Lake, AZ. Both lakes are just north of Yuma. It's over 125 miles of big flat water, with huge current, fluctuating daily between about 5,000 and 11,000 cubic feet per second. (Gotta irrigate all that lettuce!) Info from Yuma BLM: http://www.blm.gov/az/st/en/fo/yuma_field_office.html
Pretty good Lower Colorado River map with boat-in camping areas shown: http://www.fishnmap.com/catalogframe.php
Punch in "Arizona" and "Lower Colorado River."
You can tell I'm daydreaming of this trip! It's popular with Boy Scouts, by the way. You'll see flotillas of Grumman aluminum canoes on the river at Thanksgiving, Christmas break and Washington's birthday weekend. They get their "50 Miles Afoot-Afloat" patch canoeing the river. Since most Arizonans don't acknowledge the Lower Colorado River region as being part of their state, most of the Scouts I've talked to are from California.