They likely have a financial aid package that will help them pay for rent.

If they are getting student aid, you can also require a current copy of their current financial aid letter.If they are international students, have them prove they are a student in good standing and show you their student visa in their passport.I also learned that grad students are much better than undergrads. 

Be mindful that there are several advocacy and legal aid groups only too happy to assist any tenant applicant who is told by a landlord that service animals require a different rent or deposit, or that the landlord will not make a reasonable accommodation. 

The closest we've gotten is tenants depositing into our accounts at the bank.- You will be limiting future applicant pools if you refuse to take cash.  

You can not only lose the entire deposit, regardless of any justified deductions or rent that was due, but you can end up having to pay them twice or three times the deposit plus court costs, depending on the jurisdiction.The tenant doesn't even have to be savvy - they can just go to free legal aid for help ...

Ridiculously stringent criteria are so crazy that nobody meets the minimum qualification, thus you pick the one that comes closest - but if there should be an applicant that does qualify then you accept that applicant. 

This is a great idea, I'll see if I can put up a flyer at the closest schools etc.

Although they were good about sending their maintenance staff right away when there was a problem, they only did quick "band aid" fixes instead of fixing the actual problem.For example, my second summer there, 1x/week my A/C would suddenly stop blowing cold air. 

So far, all of our students have gotten financial aid, so they budget for rent right up front.

@Geetika Casmon  According to this Illinois legal aid website, no notice is required to end a lease.