All U.S. Embassies and "most" consulate or satellite office will have a U.S. banking facility in them. So you can visit the embassy or satellite office and purchase a pre-paid VISA in U.S. funds. Then register that VISA online with any valid U.S. mailing address and valid U.S. phone number. It can take up to four hours for your registration to propagate where ever it needs to across the Internet. Then you can use that pre-paid visa to pay your online fees.
Online registration instructions are included with the card when you purchase it. So you will "activate" it before you leave the bank. Then you will "register" it with US billing information on the Internet, when you get back home with it.
I have another question. I have managed to get to the payments being done but after that it won't let me get to the e filing part as it keeps telling me I have left out some information asking for my state and zip which are different from US ones as I live in a foreign country. Can anyone please help me with this. I am going crazy!