Hi Karen,
Strollers are available for rent at a variety of locations throughout Disney Theme Parks, Disney Water Parks and the Downtown Disney Area. Quantities are limited and subject to availability. (Double-passenger strollers are not available for rent at the Downtown Disney Area.)
The stroller rental fee is:
$15.00 USD per day for a single-passenger stroller
$31.00 USD per day for a double-passenger stroller
$100 USD credit card deposit is required per strollers rented at the Downtown Disney Area. (The rented stroller must be returned to the original rental location to receive a credit card deposit refund.)
For Guests who require a stroller rental for multiple days, a length of stay rental ticket is available where you make a one-time payment transaction for as many days of rental as you will need. Upon visiting a Disney Theme Park, show your receipt at the stroller rental location and you will be expedited through the queue with a reduced wait time.
The multiple day rental fee is:
$13.00 USD per day for a single-passenger stroller
$27.00 USD per day for a double-passenger stroller
I would definitely consider bringing your own stroller from home if you feel that your child will be more comfortable as the rental strollers are made of a hard plastic.
Wishing you a magical trip filled with memories which will last a lifetime!