Running a good rental business sometimes requires that you NOT throw out the baby with the bath water meaning sometimes its better to stand with people who have a track record of paying you but run into financial or health issues.  

Deny them based on his credit and eviction.The next place they apply, they will probably just not tell the landlord about the baby daddy, and he'll just move in after she gets approved.  

My cheery personality around here is all natural baby.

Not very many of us skip the “baby steps.” 

Point is, the borrower's were to some extent targeted to be able to go through the entire program including the rate increase.HAMP is a government baby, it was criticized by many and still is.  

My wife and I lived there previously and we had a dog and a baby which took somewhat of a toll.

Young, old, female with babies, whoever!

And again those are situations that you as an individual work out in your own way given your financial condition and how you feel about a certain tenant.. my classic was the tenant who told my PM they just had a new baby ( which I believe they did) record cold winter they could not afford heat and rent could I do something.. so of course I say sure.. don't pay two months and add it to the rent and pay over the course of the coming year.. end of two months they up and left  LOL. and for sure I can see how investors that are highly leveraged with little to no real reserves might react differently than those who might own the real estate free and clear or if they missed a month or two of rent its just no biggee 

She apparently had a baby in June as well.

Think, "I love beanie babies.