Check with PayPal. See if there might be something there. I know that is where I have a couple of accounts on products I sell for other people.

There are many ways this could be handled, but it would need to be initiated by them.
Almost any business can hire independent contractors although I do not know their corporate or accounting structure. You can be an independent contractor and receive commission without being a direct employee. You would be a self-employeed person responsible for paying your own taxes, expenses, etc. They would not deduct employee taxes and benefits from your paycheck (like Social Security, Insurance, unemployment ins, govt payroll deductions, etc) You would have to pay all those items direct through a mandatory self-employment tax. They could create an ID # for you which could be part of your link and know if a customer came through your website. Perhaps a set amount or finder's fee would keep it simple for them. There are tracking softwares out there... These are just some ideas... I/ could write for days about this but don't have the time... hope this gets you started.

If they want to establish an Affiliate Marketing program...I do not know the ins and outs or cost of creating such a program... But I imagine it takes some time as their are legal binding contracts involved... They must be approved by the companies that handle these types of programs... such as clickbank, share a sale, commission junction, etc as they are able to address the international issues involved, exchange rates, and verify the viability of a company to insure the company is legit and that their affiliates get paid, etc. There are no guarantees, but these compnaies will do their homework before they agree to represent a product.