The hotels do not offer them. If you have a small child, I would bring your own.
Stroller rentals seem to move based on how busy things are. There is either a location inside each park or a tent between the two parks. Then tent between the two is during the busier times. Strollers can be taken back and forth from one park to the other, but not out of the security gates to the hotels or into Downtown Disney. Besure you keep you receipt, that way if you stroller is lost, taken or you leave and return on the same day you can get a replacement.
You can also rent strollers at the star trader store. Ask at the back register and they will get one out of the back room for you. YOu can also get a "replacement" stroller there with your reciept.