If it isn't working, it's because of the banking system somewhere. We just ask for authorization and they say yes or no.
That's only partially true. Yes, the problem is caused because of the banking system situation but today, many websites (possibly more than 50%, at least in my experience) work without problems (sites that previously didn't work when this situation began). So, it's up to the websites themselves to lift the restrictions, too. Can't say how this works of course.
You would need to set up your own Paypal account. Normally that's not difficult, but maybe Greece is different right now.
I do have a PayPal account, and a direct transfer from my PayPal account (which is linked to my Greek card) to your PayPal account/email would work (PayPal has been confirmed as working here for such transactions). It doesn't work for JRiver now, because even the PayPal method goes through your current billing systems (which currently don't work with Greek cards) - it is not a direct PayPal to PayPal transfer.
Anyway, I'll probably use a relative's non-Greek card to bypass this problem - I hope other users can find similar solutions.