I would have one partner create a separate page/contact form specifically for the advertiser – so only people who see that contact form are people who were referred to by the advertiser. The advertiser would use that page as their outbound link. I know you can track outbound clicks in Google Analytics events and Contact Form conversions (usually through most contact form plugins) but that is the best way I think. Never done it, but this is how I see most affiliate programs like that work.
I would personally agree with linkshare.com as a great affiliate marketing platform to join as a publisher. Here’s why. Back in 2005 when I knew nothing about affiliate marketing and was using blogger.com as a free blogging platform without any experience whatsoever and joining Walmart.com as my first official affiliate program, I was able to insert Walmart affiliate in its in my blogger blog and earn a $72 commission. I was onto affiliate marketing for life from there.