This is not unique at all. Getting applicants with low credit scores is something that happens all the time.
Obviously, you allow and consider co-signers (otherwise, why would they have one?), and the cosigner meets or exceeds your criteria. So what's the problem?
Your tenant screening criteria should be crystal clear on what your requirements are, and they should be applied consistently to all applicants in order to avoid fair housing and discrimination complaints.
The fact that you are asking us to interpret your screening requirements is cause for concern. (I'm not knocking you, simply pointing out that you may want to tighten up this process), for the following reasons:
Let's say you ultimately decide to deny these applicants housing because you just aren't comfortable with the whole cosigner thing and don't want to deal with it. And let's say they are of Asian descent (of course, I have no idea, I'm just making up an example).
Then another month goes by, and you get a similar application from a couple who are not Asian. Low credit scores, but an otherwise decent application with a solid cosigner. After losing another month of rental income to the vacancy, you're under pressure to get the place rented ASAP, so you cave in on the cosigner thing and rent to them.
The first couple now has reason to believe (and possibly evidence to prove it, even if it was never your intent to discriminate) that you denied them housing because of their race. After all, you rented the exact same unit to the other couple in the exact same circumstances - The only thing different was their race.
You end up in court, and the judge asks you if you have published screening criteria ("Yes your honor", and whether you understand and apply them consistently with each and every applicant ("Yes your honor").
But then the plaintiff's attorney shows the judge a printed copy of this thread from Bigger Pockets, which suggests you were winging it and asking for advice in a public forum about how your own criteria should be interpreted. This makes it very hard to claim that you always apply your screening criteria consistently, especially when you literally didn't apply your screening criteria consistently.
Again, I'm not knocking you - You haven't done anything wrong and this is all hypothetical. We are all here to learn and exchange ideas. I'm just pointing out how these things could be interpreted in a worst-case scenario, and highlighting why consistency is key when it comes to tenant screening.
BTW - An increased security deposit is a great way to mitigate the risk with these applicants, as noted above. But that too needs to be spelled out in advance and applied consistently to all applicants.