If you don't like the terms, move on to another "landlord".
I prefer taking (and using) paypal, for the convenience of it all. I will also accept a check, but it is more cumbersome. Remember, though, that you are renting from an individual, not a business, and not many individuals have merchant accounts with visa/mc/amex/etc. So, with a very few exceptions, you're not going to pay for a point rental with a card without an intermediary like paypal processing the transaction.
This is one of the many reasons why point rentals are such a screamingly good deal for the person doing the renting.