Yes, they have strollers in concierge (they will tell you on a first come, first serve basis - we've been twice and were able to get one both times). We were there 4 weeks ago, the entire resort was full, but we still got a stroller and there were a couple there all week long not in use. They have the jogger stollers. They are a pain to fold up, which you have to do if you take the boat or the train (not the monorail). They had ONE of the jogger type without the big front wheel. It was a bit beat up, but we took it instead of the big wheeled type. It was soooo easy to fold up and a lot easier to "drive". The basket in the bottom has a whole from too much wear and tear. We rigged a towel to it with pins (bring large safety pins with you if you want to get this stroller). Once we did that it was great.
have a great time!