I use PayPal for my check-out process. Overall, it works great, but the discount process can be a bit confusing.
It will seem as if you aren't being given a chance to enter the discount, but once you enter in all your payment information, in the next step, it will take you back to the store where you are given the opportunity to enter the discount code and it will be applied.
(Note: I've changed site design since these instructions, so it may look slightly different, but the basics are the same.
I know, it takes a little leap of faith to trust that you'll get the chance to enter the discount after you've entered the payment info, but it does work. If you do make a mistake and miss it, just contact me and I'll rectify it.
Note that it shows you the regular amount and you have a place to enter the discount code. Be sure to hit Apply!
Once you see that your discount has indeed been applied, hit Complete my purchase below.