Recommendations for a WordPress Plugin

A client of mine is a Beauty products supplier and they have asked us the following question:

“We are getting asked by beauty training schools if they referred us to their students, could we offer a discount and a kickback credit/cash for doing so.

Is there any way we can do this and keep track of the spending against a code?”

I have looked at affiliate program plugins but none of them seem to do what the client is wanting. Maybe I’m looking in the wrong area and should be looking at coupon plugins – or is there an alternate way we can achieve this like by creating a form on their website for referrals?

Thanks in advance.