Why is your tenant paying you by credit card? 

They look at your credit profile and get you business lines of credit and credit cards.

I have done it with some contractors taking Paypal where you can use a credit card on that site with a fee, or QuickBooks is another one too.

For context I am a full time lender and understand DTI and have very good credit. 

@Donald Hatter We send the information to a collection agency who attempts to recover the money; after they make several attempts they place it on their credit report. 

@Ryan Vienneau I'm a Buildium customer too, and it blows my mind they don't have credit card tracking in 2017.

Quote from @Carlyn Chism:I agree with Chris on a lender that might be a scam or make you may so much money interest because of the low credit score that you make $1.00 on the flip or no money.  

U will never get a dime of rent and you are going to have to probably do as you stated find your own attorney.. its better to leave property vacant than to rent to folks that have terrible credit.

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

Seller financed (probably) won't be reported to the credit bureaus and so won't impact your credit score at all.