Should I rent to tenant with 540 credit score

[Bill Briscoe]

I have 1 property which rents for an above avg $1275/mo, SFH, tenant pays all utilities, yardcare, etc. We did a full reno 3+ years ago and have a mtg so cash flow is only about $450/mo.

So far we have had 3 tenants - all of which have been very responsible and had credit scores over 700.  Now it is vacant again and our only applicant in 6 weeks has been a single mom, 2 older kids, recently divorced, and with a credit score of 540.  Income is $50K so she makes the 3x ratios barely, but that comes from 2 jobs, the 2nd of which is a newly opened bar so she only has 1 paystub year-to-date.  The other job is leasing manager at her current apartment.  She pays that rent "on time" but it is a payroll deduct, so it would be hard/impossible to pay it late.

She is very interested, and paid the $39 background fee check, so I want to work with her, but don't want to take on a completely stupid risk. Thoughts on this one? 

Would you approve her?

Ask about a co-signer?

Deny application initially but offer approval with deposit plus 2 months rent up front?

Something else?