I've used Money Orders in place of Paypal on "that site" for several transactions.
When the auction ends, I contact the seller with the request to use a Money Order for the transaction. I don't even use "that site's" - Contact the Seller as "that site's" police may get wind of using an alternate form of payment and could shut down both seller and buyer. As long as the seller knows, up front, then there shouldn't be any problems. The sellers I've contacted to use a Money Order all hate Paypal anyway, so that isn't much of a problem. So far, I've encountered no problems with "that site"...
I've been trying to "wean" myself off "that site" anyway as both "that site" and Paypal are very anti-gun.