Sometimes you can come across a newly hired cashier who is not very familiar with the store’s policies, and who will refuse to accept your coupon, in which case, the smart thing to do is to ask to speak to someone in charge, a manager for example.
Make sure you stay calm and collected, and don’t back down easily.
Before your shopping trip, don’t forget to do your homework! Read the fine print on your coupon, call the store and ask, email them, send them a snail mail if that’s what it takes! There are indeed some stores who really don’t accept internet coupons; so unless they change their policies especially for you (very unlikely), you’re out of luck!
In other cases, you might want to put on your “Rambo” outfit and further argue with them (always as calm as possible). You better bring evidence that a particular store allows coupons (a printed copy of an email they sent you, for example), so you can strongly plead your case.
Ok, I know this sounds like you’re in court, but it’s actually very similar!