How anonymous do you want to be? Are you trying to hide from the recipient only, or also from their payment processors, or the government?
Each of these requirements has different solutions.
Each of these requirements has different solutions.
I suspect a sibling comment is correct - buy a visa/etc giftcard (perhaps with cash) and use that to donate online if the recipient accepts online payments - or send the card details via email, or the card via snail mail?
> buy a visa/etc giftcard
I like that suggestion the best as well.