The only discount I know of for strollers is the length of stay discount. Just tell the CM at the pay line how many days you will need a stroller. The CM will give you coupons for each days stroller rental. I believe you will get a 20% discount. You won't have to go through the pay line again during your stay which will save you time.
I don't know how many days qualifies you for a length of stay discount. Check with the CM when you pay for your stroller the first time during your visit to the World.