An alternative approach would be to create a 'claim coupon' form and point your couponeers to that so that they may redeem the coupon. The trickier part would be then to keep track of the coupons in a similar fashion to the 'Items in Cart' (either via session based tracking or link it to their account).

This approach would also allow for implementing coupons in different ways (ex. time-based, limited), reduce mental stress by being able to retry codes till you found a valid coupon (some providers allow for coupon codes but no way to verify it's valid) and not distract from the check-out process (it would simply require showing which of the redeemed coupons are applicable to the purchase).

A plus side of this approach is that a coupon is enough to persuade potential buyers to create accounts to keep their coupon (while it's valid - for later use) and thus also reducing friction in the check-out process which should lead to more sales.

I do also now believe the existing 'coupon' implementation is at fault by leaving too much on the table.