This is copied from the stroller section of Disney's website if you're interested in getting one at the parks:
Single Stroller
Recommended for children 50 lbs. or less.
- Daily: $15
- Multi-Day (Length of Stay): $13
A $100 USD credit card deposit is required for strollers rented at the Downtown Disney area.
Double Stroller
Recommended for children 100 lbs. or less.
- Daily: $31
- Multi-Day (Length of Stay): $27
Length of Stay Rental
Pre-pay the number of days that you will require a stroller and save. Purchase a Length of Stay rental ticket for less per day when rented for multiple days. Then, upon visiting a theme park, simply show your receipt at the rental location to receive your stroller for the day.
Stroller Return and Replacement
Strollers should be returned to a rental location before leaving the theme park.
Stroller Replacement
Strollers cannot be removed from the parks. When visiting more than one park in a single day, simply present your rental receipt at another park to obtain a replacement.
Likewise, if you misplace your stroller, replacements are available with a receipt at various locations throughout the Resort, based on availability.