At the one by me, they don't, but if you belong to their rewards program (yes, with that nifty little keyring or wallet card) you should receive 20% coupons in the mail, continuously. That has been the case for us, at least. We never not have a 20% BRU coupon. Plus, they send me a bunch via email.
It depends on when you go... if you go when a new set is out, sometimes they'll scan that for you. At least they do that here, especially when I pull the "shoot, I left mine at the house."
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I overheard a sales guy at BRU saying that the 20% off coupons don't work for Gliders b/c they're not considered to be a "baby item". I wanted to use one on a new glider myself. I would call the store near you and ask to make sure though.
Tell them you have one that you got in the mail, but accidentally left it at home. Depending on the mood of the clerk you get, they might be nice and just scan one for you. That happened to us when we were getting our Angelcare monitor--we really did have a 20% off coupon, but not with us at the time, and the girl scanned one that they had up at the checkout counter.
Go to the Customer Service desk or Registry desk and they should give you a booklet with the next set of coupons. The only thing is they might not be valid for another couple of days depending on when you get them.
Re: Babies r us
Not the one by my house