You need to make sure that you meet your debt service, and that you would continue to be able to meet your debt service (plus whatever coverage requirement the lender imposes) even if occupancy drops during a downturn.  

See http://www.csatravelprotection.com for details about this coverage. 

What kind of coverage is out there and, in general, what does it cost?

I just became aware that she had no insurance coverage.  

Its likely  you will need to have the home and the rental dwelling in different companies to get the best price/coverage.   

They will deny you coverage after they find you turning policies in 1-3 months.

Typically they want to see over about a 1.25 debt coverage ratio. 

The fact is all that is needed is adequate insurance coverage, Insurance is always the first line of defence and all that would ever be required initially.

Lenders will look at (1) track record of sponsor (2) credit worthiness of sponsor (3) amount of sponsor's cash investment in deal, (4) terms as spelled out in PPM and Operating Agreement, (5) legal compliance as to Federal and state Securities laws, (6) experience and reputation of securities attorney representing sponsor/syndication, (7) legal audit to determine likely hood of lawsuits by investors, (8) profitability of property (9) debt coverage ratio (10) return vs risk analysis (11) property appraisal.

It reduces administration ands give you liability coverage for 30 days on "Newly acquired" properties, so you don't have to sweat adding a property in time.