It should be noted that cookie stuffing is a term for a specific process where a site will inject cookies for thousands of sites with their own referral code on pageload of a landing site they control. It is highly illegal and people have served jail time for it, as it is considered fraud.
What coupon sites do is they tend to hide codes behind a button that onclick will load the retailer's site with their affiliate code, then show the code.
There's a lot of forms of cookie stuffing that are legal, or at least grey, and still seem to me like cookie stuffing, even though they aren't standard, clear-cut, illegal cookie stuffing fraud.
I usually try to build flows now that don’t ask for coupon codes at checkout (because that leads to deal searching right at the last moment). I prefer dedicated URLs with embedded offers as much as possible.
If you need to go the coupon code route, I recommend how Namecheap does it: they registered a unique domain (namecheapcoupons.com) that publicly list all coupon codes. They rank #1 in organic search results.
But, as a general rule, I encourage you to avoid working with deal sites and coupon affiliates. This is a general rule, but they tend to drive very little incremental revenue. You should also disallow any PPC campaigns using your branded terms.
The overall affiliate channel has become increasingly challenging to manage profitably from a merchant perspective. But it’s very easy for a “manager” to see all of the sales affiliates “drive” and assume that it’s making them money.
If you let affiliate sell for you, you had better invest in a professional affiliate manager that you can trust. If you source it to an intern you’ll lose a ton of money to leeches and fraud.