User Referral? Invite? Invitation Voucher? I need coupon codes!

Help!
It looks like there's a mind-boggling array of choices to approach what I'd like to do, but none of them exactly what I want as far as I can tell. Can someone help point me to the best "jumping off" point?

What I'd like to accomplish is give each registered user a "coupon code". Any new user who registers can enter this coupon code and the owner of that code gets a slice of any purchase that the new registrant makes. Now "User Referral" is very close to this and I could easily adapt most parts of it, however the having to register through a specific link (as opposed to having a "Coupon Code" text box on a 'regular' user registration page) might be a bit cumbersome.

Would "Invite" or "Invitation Voucher" be more appropriate? Or should I just hack "User Referral" to allow the referral code to be used as a coupon code on registration as well as the regular link?

Mark