What I have read in your post is that you have screening standards but are prepared to completely ignore those standards and accept a applicant that does not even come close to qualifying. If that is the case you are off to a very bad start in this business if you go down that road.
If you have screening standards why would you be considering accepting any applicant that does not qualify.
If you compromise your standards you are opening the door to failure. Don't ever try to find ways to make a clearly unqualified applicant fit. Co-signers do not provide you with any more security.
You need to add a new screening standard...we do not accept co-signers.
Why are you wasting time on this applicant, are you a despirate landlord ????. Pass please.
@Thomas S. is correct: set standards and hold to them. There are times to deviate, but they should be rare and for good reason. These tenants have multiple red flags:
1. ESA is an indication she doesn't mind cheating the system (most likely scenario) or that she has mental issues that can affect other areas of her life. You can't discriminate against her or the animal, but it's a red flag to watch for.
2. They are young which means they are unproven.
3. They have no credit or bad credit which means they are unproven.
4. They are roommates which means they are pooling resources to afford something they normally couldn't. There's a good chance the relationship will fail, one of them will leave, and the remaining tenant won't be able to afford the place.
5. I'm sure they know pet-friendly rentals are difficult to come by yet they both have animals. This inability to delay personal gratification for the purpose of securing affordable housing demonstrates immaturity. I see it all the time in every age group but young people are especially bad.
Sorry, but I would give this a hard pass.
I love pets. I think most pet owners are responsible. With over 300 rentals under management, I honestly can't remember the last time a pet caused damage that wasn't covered by the tenant and/or their deposit. I encourage owners to allow them because they can typically make more money and tenants tend to stay longer.
You have to establish standards that mitigate your risk and then stick to them.
Totally agree with @Thomas S. and @Nathan G. There are too many renters out there looking for a nice place. At least in our area, we have so many qualified people looking, I would never settle for less than my requirements. Like Nathan said, they are unproven people (financially speaking). Why would you take that risk?