The tracking is easy for online stores. However you are facing local vendors who only close deals behind the counter, it's rather a challenge.
A simple way is to rely on the vendors to report them to you, like Javier said. However, when you make money by commission, your earning will highly depend on the vendors' honesty and motivation. That's not so reliable as a business model.
Did you ever consider another model? That is, instead of earning commission, you charge advertising fees. That will make things much simple, and easy to scale.
You'll charge the vendors by the position and duration of their coupons on your site.
You help them to design the coupon banner to make your site's looking consistent.
The vendor knows their fixed cost(the ad fee on your site), so they may make more aggressive discount to get the cost back.
You show off your traffic stats, promotion plans and case studies to increase fee in the future.
To get traffic, you can:
Spread prints on the street.
Advertise your site on local new paper, local classified.
Advertise your site online by targeting local visitors.
In the future, you could try more interesting ideas such as a mobile app to show coupons when check-in etc.
Just some ideas for your reference.
Reply to Stanford's comment
The comment form may be short, so I reply here.
No matter upfront or commission, the end result will all depend on the promotion effectiveness. When you use commission model, you'll still have the concern of losing your own investment. The risk is transferred to your side, but the nature is unchanged.
I suggested ad model because there is no easy way to track local vendor sales, to my knowledge.
When using ad model, the only thing you can track precisely is how much coupons of each id get printed. When time passing, you may also get a rough idea of how each type of coupons converted, by visiting vendors and talking with them. Something may convert better and something may be less, you'll have the rough picture.
Now back to the question.
If you feel hard to persuade clients at initial stage, and that should be, you can offer a free trial or a big discount for trial to kick-start. You'll see the numbers how many coupons printed, so you'll know if your efforts take effect or not, no matter clients pay you or not at this moment.
After you have numbers(the printed coupon and visitors etc), you'll have something to show off and be confident.
Some Future Idea
Some other ideas for your consideration after your initial success, and have time/money to invest on some technology.
Limited quantity coupon: The visitor see the coupon, click print, the system ask him to verify, say a mobile phone number. After verified, he can print the coupon, and coupon quantity displayed will be decreased by one. This is powerful than plain coupon.
Direct deal: You establish a mini e-commerce system. Visitor see the deal, buy it, get the receipt, and then use receipt to consume the vendor's service or product.
Hope these help.