<i> They'll probably even require me to send them an f'ing paper check too. </i>
I've been temporary renting my old house, and I don't take credit cards, nor am I setting up a custom merchant/billing/etc system for one renter. Mostly because all the easy solutions eat a percentage of the transaction.
So, outside of the initial cashiers check for the security/etc depost, I've been willing to take direct depost, or any other electronic form of payment that can deposit money into a checking account I've setup.
Funny thing is, all of my renters so far have ended up sending paper checks. Including the first one who also happened to be a pretty serious software engineer. That is despite the fact that there are a dozen billpay/etc services and various electronic transfer/etc services in existence. Overwhelmingly they are ripoffs, and the few run by honest banks in a number of cases actually send paper checks if the bill isn't for a major credit card company.
Try it. Can your bank send a thousand dollar plus amount to a random 3rd party bank/account for free (or a trivial fee?). I doubt it. For whatever reason setting up a funds transfer between two arbitrary checking accounts is more difficult than it should be.