According to Mousesavers......Disney rents strollers at $10 per day for a single, $18 per day for a double. There is a discount for multi-day
stroller rentals that works out to $8/day for a single, $16/day for a double.
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We rented a double stroller for our DS4 at the parks from 10/26-10/31 and got the length of stay rate of $8 per day.
OP, how old is your child/children? Reason I ask is that the park strollers are very durable and can handle younger and older children more so than a regular stroller you would buy in say
Walmart for example. Our DS4 is too tall and, IMO, too old for a regular stroller (he was out of them by 3 years old). But the park strollers were perfect for him and he didn't look to tall or too old in them. There was no way our DS would be able to walk around the parks without one. It's just too much for him.
One other thing to note if you decide to bring one of your own. You would need to carry it on the Disney transporation (especially at MK where you would be taking the monorail). When we used the busses, there were a few families that brought their own stroller. We could see the frustration on the parent's face as they were trying to get it on and finding a place to set it down without hitting anyone.