This does depend entirely on where you are, as the laws in each place will be different. From your mention of customers "coming in to redeem them" I'm assuming this is a local thing with physical stores, which probably makes it easier if there's only one set of laws to deal with!
"Discount Clubs" and "coupon books" have been an area for scams in the past, so some places have laws that specify how things should be done. It's more to protect the consumer than you, but if your area has such regulations you'd need to follow them.
Here's an example for Discount travel clubs in Alberta. In another example, Wisconsin has a law that specifies exactly what must be in the contract with the consumers, and also in the contract with the merchants.
You might be able to find some examples by searching for "coupon book contract" (even if your discounts are not in a book, the idea is the same). But, given the way there are clearly varied and specific laws on this subject, you'd be taking a big risk to use an example from another jurisdiction.
This is one of those cases where local legal advice may well be needed, or maybe go for something else instead if that makes it uneconomic. As you realise, it's tricky getting the merchants to perform, quite a high risk of upset consumers, which is why third-party discounts have become regulated in some places.