Most banks will require that you provide earnest money in the form of certified funds, not a personal check.
In fact, I've never seen a bank allow an REO to be purchased without depositing certified funds in the account of either the listing agent or the title company.
I agree that most of them want this, however, I do have to say that I have personally written a check from my business account for the initial EMD and also submitted my POF with it. In several cases, that was all that was needed and the escrow company cashed the check. In other cases, they have required certified funds to be deposited and the original business check was written, but only a copy of it submitted with offer so it was just voided and certified funds replaced it when the time came.
Either way, I agree with J that banks will want certified funds most of the time and I have NEVER heard of a promissory note for an EMD. In this situation, you are dealing with banks and not private owners where you can stipulate ANYTHING with them.