Three south rim options in ascending order of difficulty:
For those in casual backpacking shape:
-Main corridor, something like what Eric suggested above. Getting campground space in mid-Sept might be tough.
For those in good backpacking shape (can do a 20 mile day in the Sierras, no problem):
-Down New Hance, across Tonto, up South Kaibab.
For those in serious backpacking shape (30 mile days in the Sierras), with good nav skills and at least one rock climber in the group:
-Royal Arch route, you'll need a 4x4 or a Suby and a good driver to reach the TH. Amazing, amazing hike. Rugged off trail hiking, exposure, and one baby rappel.