This should be possible using a custom field to hold the affiliates ID. I recommend doing this with ListMail's "unique ID" for each user, which can easily be inserted into your emails using a message code.
To track subscribers, have your affiliates direct prospects to a page with their UID, such as
http://site.com/refer.php?id=1a2b3c4On that prospect page, populate the value of a hidden field named "user1" (Custom Field 1) in your ListMail form.
After that, to send the emails, you would need a custom script set up in "signup-xtra.php" in your main ListMail folder. (see ./xtra folder for details). You would also need a custom script (or simply a custom MySQL statement in PhpMyAdmin) to list your affiliates along with their number of referrals.
I could help you out with this for a reasonable fee. $50 sounds about right. You can contact me by email at deanATlistmailpro.com and paypal at paypalATlistmailpro.com
Regards