New York, NJ and most other states have Blaine amendments to their constitutions which forbid vouchers to parochial schools (They were written against catholic schools not jewish) and because of the way they were written , it would take a entire re-writing of the New York Constituton to undo it.
To the best of my knowledge, New Jersey does not have a Blaine amendment.
As for amending the Constitution in New York, it would not take an entire re-write, but the amendment process is, at a bare minimum, two years long and unlikely to succeed.
The Wolf