The most convenient is at the Disney Car Care Center. They have a shuttle that picks you up at the Fort, and brings you back to FW after you return the car. That is through Alamo or National, whichever you choose (they are the same company), the signs all say Alamo but you can also reserve through National.
All you need to do is use any house phone, at the Fort to set up your pick up. I think that there is a special button for Alamo on the house phones.
You can also rent through most of the other major companies. Most have stations at the hotels at Downtown Disney (Hotel Plaza Blvd), you can take a Disney bus to Downtown Disney and the hotels are right across the street from the Market Place bus stops.
Downtown Disney Hotels with Car rental desks are as follows:
Hilton Orlando (AVIS)
Buena Vista Palace (Alamo/National)
Regal Sun (Dollar)
Doubletree Hotel (Budget)
Others include:
Dolphin (Alamo?National)
Shades of Green (Hertz)