I just googled and found this one:
http://grandcanyon.com/white-water-rafting-tour.html

Thanks! But WOW that's expensive. Maybe we'll have to try California.

This trip is flat-water from Page, below the dam to Lee's Ferry (the normal put in point for boats doing the main canyon).

There is no white water and you aren't actually in the Grand Canyon but the cost is OK and the scenery is beautiful.

http://www.raftthecanyon.com/

I have done the 3 day trip. Even one that is 3 day is very very limited. To do it right, requires 10 days or so.

Thanks Bill_H. That's an option. It may be too far from the south rim, but if we go around that way we can go on to Las Vegas...

The one WhereAreWe linked to is not direct with the outfitters but a third party who would take you from Williams and charge you more. If you are wanting that same trip and are willing to drive yourself to Peach Springs then you could book direct with the Hualapai tribe and save some money:

http://www.hualapaitourism.com/rafting.php

"... you could book direct with the Hualapai tribe and save some money"

If I did the math right they're charging almost $400 per person for this, which is a gigantic rip-off. This is the very tail end of the 'normal' 225 mile Grand Canyon rafting trip, where the smaller non-motorized boats pull out. There are only a couple of mid-sized rapids below this spot (Diamond Creek) before you are in the flat water caused by the back-up from Lake Mead, so you are not really getting much of a 'white water' experience, especially in a large motor boat.

The one-day trip from Page is easier to get to and costs about $80 per person instead of almost $400. And has better scenery. Also there's enough to do at Page to warrant a day on its own, unlike Peach Springs.