Newbie-1st time Landlord / applicant conundrum

[Cindy G.]

OK, Here are our issues:
4/2.5 house we entirely rehabbed ourselves. Our first one ...

Applicant wants a 2 yr lease, $1,125 yr 1, $1,135 yr 2
Family of 5.
Husband getting job transfer, making $50k gross.
So we used TransUnion SmartMove, got the big red DECLINE
[i]Level of delinquency on accounts
Too few bank revolving accounts
Number of accounts with delinquency
Inquiries impacted the credit score[/i]
BK in 2005:
Plus...
Scores of 580 + 591

Husband has 12 year job history w/same co., so does wife, but she has no transfer of job lined up.

What we have read on BP is many of y'all don't just use the score to eliminate ...
Do we even explore further?
Do we have them get a co-signer? (out of state)
Thanks
Cin.