Copied from the Dis site:
Disney World Stroller Fees:
$15.00 for single - $13.00 per day for Length of Stay rental
$31.00 for double - $27.00 per day for Length of Stay rental
When purchasing a Length of Stay rental, you show your receipt and can bypass the queue with little or no wait.
However, I'd recommend a stroller swap first, and if one's not available, Orlando
Stroller Rentals. I recommend this for a few reasons:
1.) Much more affordable than park rental
2.)You have it outside of the parks as well if needed
3.) Saves you the trouble of lugging one through the airport
I am in two stroller swaps, one is $15 for my entire stay, the other is $10 (possibly increasing though). My feeling is, for the price of 1 day in the park, the stroller swaps are the most affordable way to go and get a decent stroller that reclines, maneuvers easily, and can hold bigger children (many use it for 6,7,8 yo's).
Good luck. I hope the info helped!