Yes, you may rent strollers, wheelchairs and Electric scooters at Downtown Disney, however their rental policies differ from the parks, as Downtown Disney is not gated.
The rental of strollers, wheelchairs and
ECV's are first come, first served, and are not reserved for guests ahead of time. They are in limited quantity, so if a wheelchair is a necessity, it is probably a good idea to bring one as having rented one in the park that day is not a guarantee that one will be available for rent when arriving at Downtown Disney. If a stroller becomes a necessity, and the guest doesn't bring one, and one is not available for rent, they do sell umbrella strollers at Once Upon A Toy.
There are no double strollers available at Downtown Disney, they do not fit in the shops.
Strollers and wheelchairs must be kept with the guest at all times, and may not leave Downtown Disney property.
The rental for Strollers and wheelchairs is $10 like the parks, however you must leave a copy of a major credit card on file at Guest Relations as a security deposit. If a guest decides to keep the wheelchair or stroller as a souvenier, then their credit card will be charged the replacement fee of $250 per stroller or wheelchair. Rental for the ECV is $35, but if it isn't returned, the replacement is $500.
Length of stay rentals are accomodated for wheelchairs and strollers, however, that doesn't guarantee that a stroller or wheelchair will be available, see above. Also, the credit card copy is still required for a security deposit.
All strollers and wheelchairs must be returned to Guest Relations by 11 pm, regardless of day of week or location. ECV's may only be rented from the Marketplace location and must be returned to same, also by 11 pm.
Strollers are not permitted in Disney Quest, so if that is the plan, the guest will need to please return the stroller before going in. Stollers are also not permitted in the shop Starbillias in the Westside, which is across from Guest Relations... so either make that your 1st stop on the way to rent, or your last, after you have dropped off the stroller.
When strollers, wheelchairs, or
ECVs are returned, the guest is given the copy of their credit card back, as long as they return it to the same place it was rented. If not (doesn't apply to ECVs, as they have to be returned to the Marketplace), the guest will not receive the hard copy of the credit card copy... the castmember will call the other location to let them know the wheelchair/stroller was returned, and the credit card copy will be shredded.
Hope this helps. I know that many guests get to Downtown Disney and don't know these things, which can be a rude awakening, since the parks all have many, many strollers and wheelchairs available, and are gated, not requiring such a stringent security deposit policy.