From what I have heard, there is no residency requirement in Hudson County (or at least parts of it). I know there are many students in the Hoboken schools who live in Jersey City. I'm not familiar with the details of how they enroll in Hoboken but you might call the Hoboken Board of Ed. or the Jersey City Board of Ed for more info.
Robert DeRuggiero Realtors
Here's a good place to start, if you have not already visited this site:
Prudential New Jersey Properties
973-239-7700 ext 132