There are a number of different paying systems similar to paypal - but I guess they would inflict the same problems...
Other services, e.g. Moneybookers, allow a bank transfer to a special fund, then sending that money to a person - very similar to Paypal, though some of them allow different kinds of payment.
What is his exact problem? In most cases bank transfers to a payment service should be possible from Serbia - and sending money from a payment service to e.g. you should be possible too...
Or what about services like "Western Union"? WU exists in Serbia and in the United States, and you dont even need a bank fund or similar. Your customer just walks to one of their stores (or uses their internet portal) pays them the money and they inform you about the incoming payment - which you can collect (AFAIK directly from a WU store or via internet)... At least if I understood their services correctly.
So he could actually pay cash - and you could recieve cash. I guess there are other, similar services - but I actually only remembered WU, so I hope that example is sufficient
One problem is, that Europe traditionally has a very different payment system from America - Credit Cards are rarely found - and you cant pay with them in most shops. Insted "bank cards" are used - a similar card, but instead of using a credit money is withdrawn from a bank fund.
Instead of sending checks (I dont know any bank that would hand out checks) bank transfers or debits are used, etc