There is no stroller perk at WDW for DVC members that I am aware of; however, anyone can get a length of stay stroller pass.
Just tell the Cast Member in the pay line on your first visit to the parks that you would like X amount of days for a stroller rental (X = how many days you will visit the parks).
You receive that number of tickets which gets stamped at the desk where you receive your stroller with today's date.
This provides two benefits:
1. You will not have to wait in the pay line anymore since you've already prepaid for your stroller rentals. A big time saver.
2. You will get a 20% discount on your stroller rental for the length of your stay.