Students are not a protected class but be careful of HOW and WHAT you say which can be used against you and be TAKEN incorrectly. Watch the protected classes... such as age, income (source), familial, etc.
One of the "easier" things would be that NYS has (in it's infinite wisdom) made it illegal to collect, ask or receive any additional monies other than two months of rent (whether it be first and last OR first and security).
This means that you CANNOT ask for or receive (as an example) six months of rent from a student from their loans (even if they agree to it). That is "typical" of what students would do for housing ... get their loans and pay the landlord for their semester or a year, etc. Now that is not allowed ... they would have to pay you MONTHLY.
A side note is what Deanna is saying (but again, watch where their income source is) you may be able to say no "co signors" but also as she said ... be careful about your "rules" as they would have to be applied across the entire requirements of all applicants (or it would be / could be seen as discriminatory).
For example: if you state must have a minimum of 3 years past rental history. YOUR intent may be that this will "weed out" any students for student housing. However, what if I and my wife wanted to move, we sold our house that we've lived in for 20+ years and we are not quite sure WHERE we want to move to. We find your house or apartment and want to apply. Would you allow us? We don't have rental history ...
Or, someone who went to college or worked (no college) but is on the "younger" side but lived at home ... no rental history. However, they landed this great job in your area or are "moving up" or whatever... they now have the means to live on their own and want to apply for your rental ... but they have no rental history. Would you allow them to apply?
This is where you can very easily and unfortunately be seen as being discriminatory without the intent.
--67.242.xx.xx