problem wouldnt be NY state law,
its NYC regulations you have to be concerned with,
only way in/out of Long island is through NYC,
and NYC requires rifle/shotgun permit,
only exception during transport is when it is on route,
you must be on continuous route from home to destination,
if you live in NJ and are going upstate , cop could question you why your headed to/from LI,
might up to the cops discretion,
i wouldnt chance it.