Discounts seem harder to come by at DL. As far as I know, there aren't any postcards or codes that go around like at WDW. I believe there are
AAA rates, and depending on the season, they sometimes come out with special packages that are worthwhile. A couple years ago I got a Fall Fantasy package where I paid for 3 nights and got the 4th night free.
However, sometimes there are good deals to be found on sites like Travelocity and Expedia. It seems that they are only available closer to the date of the stay, but they can be pretty substantial (mostly at Paradise Pier). From what I've seen, GC seems to be least likely to be discounted since it's the most popular (my favorite).