I don't know about you guys, but here in Estonia there's a thing called online banking? No need to go to the bank at all and maestro should also work for paypal, just change the card type (default setting is Visa, but there's options as well).
And do you even have the 3-4 digit code on the back of your credit/debit card?
If not, then maybe you can see if it's possible to make a virtual card on your bank. Virtual cards lasts for a month or two, you will not receive any plastic card, but you get all the credit card numbers, validation, security numbers, etc online. So it works as a credit card that you can use for online payments (such as paypal, amazon, ebay, etc).
Then there's always Western Union payment method, but for this, you have to speak with C4sp3r. personally, since it requires both participants to get and send eachother some information, before they can actually transfer any money.
And last but not least, you can always put some money on your phone credit and use that to donate =)