Welcome Doug! Thanks for stopping by the Disney Parks Moms Panel.
Unfortunately, it is not possible to reserve or rent a stroller in advance for Disney Parks.
Stroller Rentals can be found at Disney Theme Parks and Disney Springs, and are available on a first come, first served basis.
You can rent strollers daily or purchase a multi-day (Length of Stay) rental option. On the first rental you must pre-pay for the number of days you will need a stroller and you will receive a receipt to be shown at the rental location each day for getting your stroller. The multi-day option is a good alternative for saving a little money.
Hope this helps your planning. Please, come back to visit us again if you have further questions.
Wishing you a wonderful day.
Gina V.