Coupon is a currency in S4 League. Coupon can be obtained when opening a capsule. They usually come in pairs, with the exception of a few capsules, such as the G's Pet Capsule.
The in-game name of this item is Integrated Coupon.
This coupon can be used in the coupon Shop.
They once were used to purchase items in the coupon shop. One would go to the shop tab and click Coupon Shop. In there they would find various items to spend their coupons on. There currently 8 items to chose from at this time. However as of Patch ??, the coupon shop has been replaced and you can now use coupons in the Random Shop.