Through their affiliate network. Usually CJ, who are known for their Coupon promotions. Most the big coupon websites are able to get feeds of the newest coupons for all their merchants on CJ
Most affiliate networks provide feed with coupons / deals from their programs. The send you a file .txt, .csv, . xml. The idea is that your coupon script will need some plugin to import all coupons in a automated way as there are a minimum of 40 offers daily ( depending on the network ).