Understand how they slipped through the cracks - did you allow them to book even if you got a bad feeling, priced too low, last minute booking, etc? 

TIA There are 15% down options assuming good credit.

Consider a cash out refi, at a low LTV, say 25% 

Of course, we also need to complete background checks on each tenant, including criminal, credit, and eviction checks, and a solid lease agreement too.

The higher your credit score and the more experience you have, the better your rate will be.

I agree with @Bonnie Low. 

What I can say is that RentRedi is a complete management service that manages the entire process from marketing for tenants, through pre-qualification, scheduling viewings with calendly.com, the application, the background check/credit check/eviction check; automatic rent collection, repair/maintenance management: the whole nine. 

I think your best and maybe only solution is to put in a french drain across the yard with a large catch basin at the low point.