There are tons of Free QR code creators (or low cost).
You could create a coupon, assign unique QR codes for each affiliate (place them on cars), and scan them in store to give proper credit to the affiliates.

The only problem I see with this is: human nature.
We forget things, lose things, and show up asking about "that deal that some guy told me about."

Or

Personally, I would want email addresses to communicate with the folks. (to really measure the effectiveness of this promotion)
I'd do this:

-Create a different bitly (www.bitly.com) link for each affiliate.
-Place them on a coupon that has a great incentive.
-Write on there- redeem your coupon by visiting (the bitly link)
-This should take them to a simple opt-in page (to gather email addresses- you can use www.leadpages.net)
-They give you their email, you deliver their coupon AND you are able to continue communicating. (since most sales take 7 touches before a decision is made anyway)
-AND your affiliates get the credit without error.

You'll get the most qualified leads and you can judge for yourself how effective this will be moving forward. :)