If such is possible, you would need to program the password and Affiliate-link-provision end of things yourself, and you would need to have access to log into each of your Affiliate's E-junkie accounts, at least initially, so you could get their Hop Link codes to place into your site -- perhaps you could create their accounts for them, obtain their Hop Link code, and then forward their account info to them.
I reckon the buyer process could work like this:
The buyer would enter the Affiliate's password in your site -- you could even make the "password" something easy, like the rep's name as stated on their business card. From there, your own proprietary programming would recognize the password/name and take the buyer to a page you created (or dynamically generated) that has that particular Affiliate's Hop Link code embedded in the page, along with a cart-discount code you have created that the buyer must remember or write down, so later on, they can enter that code into their cart to redeem their discount. Once the buyer jots down their discount code, they can click the Affiliate's Hop Link to reach your shopping pages. Clicking that Hop Link will set a cookie good for the next 6 months (or until the buyer deletes browser cookies) during which period the referring Affiliate will continue to earn commissions for every Hop-Link-enabled product that buyer purchases from you.
Some possible concerns:
A generic cart discount can be used any number of times by anyone, like an online coupon, so there's nothing to stop the buyer re-using a generic code on subsequent visits (if it occurs to them to try) or even pass the code along to others. You could instead create the cart discount with a list of one-time-use codes, but there's no API to generate or populate the list of codes automatically here, so you'd have to generate codes yourself at your end and periodically post those into your E-junkie Cart Discount configs; however, you can input up to 5000 codes at once, so that may tide you over for quite a while. :^)