Yes they do. This is copied from the disABILITIES FAQs thread, post #2.
Disney has opened a small shop at the old DTD Guest Relations Office next to Restrooms and Toys for the following only:
Rental of
$15 - Single Strollers (plus $100 refundable deposit)
$12 - Wheelchairs (plus $100 refundable deposit)
$45 - EVCs (plus $100 refundable deposit)
The $100 refundable deposit is because Downtown Disney is a relatively easy area to remove things from.
They also sell a selection of baby/infant items as well as First Aid supplies to include Sunscreen and Suntan Lotion.
It is a sales and rental location only, they do not provide Guest Services but it is right next to the companion restroom at the Marketplace.
Rental Locations (besides that listed just above for DTD)
Marketplace: Guest Services (
ECVs)
Marketplace: Wonderful World of Memories (Wheelchairs)
West Side: DisneyQuest Emporium (Wheelchairs)