Not quite "on property", but Avis has a spot in the DTD Hilton, very walkable from SSR. I think there may be one at the Swan or Dolphin though..... I think I read about it on Mousesavers.com
National & Alamo (same parent company) are the official rental cars of WDW. They have 2 locations:
Car Care Center - located right outside the gates of Magic Kingdom
The Dolphin - office is located in the lobby
I use the Dolphin since it's within walking/boat distance from Epcot and Studios, but I've heard that the CCC will shuttle you back to your resort.