How do you track affiliate program conversions if you can't put code on their site?

What is a good method or system (preferably free/cheap, but good value is OK, too) for tracking affiliate conversions?

For instance, I'm trying out a money transfer aff program where I get paid for each online money transfer. I am starting out with PPC. How do I know which traffic converted into a sale?

 

Have a friend transfer some money to you - test it out if you can

 

I meant for analytics purposes. I want to see which ads/traffic sources/landing pages are performing best in terms of actual conversions.

There are scripts that will help you match traffic to actual affiliate conversions, I just don't know what they are.