Am I asking for trouble?

[Kyle Z.]

New Landlord here!

I recently took a phone call from a potential tenant, interested in my rental property.  I started running him through the basic pre-screening questions and red flags flew up left and right but I am not completely writing him off. Below i'll list the pros and cons, I would love some feedback!

Cons

he admitted he and his Fiance both have felonies

They have a Dog (husky)

No prior rental history (lived with his fiance's mom)

fairly young (27) 

Pros

They both work (will offer references) (combined they make over 3x the rent)

willing to pay asking price (I listed it about $100-$200 more than I thought Id get)

He seemed well spoken and mature

they have a 2 year old

He said his credit score is about 650 (i'll fact check this later)

Am I looking for trouble here? Is there any way I can limit the risk?

Thank you in advance