They might want to take a look at the NYS CCW permit system.
An extensive gun class is first required, then the fingerprints, then 3 character references and they better be good ones! (who they DO call), then the FBI background check.
Even after all that, the application comes back to the local police chief.
If the applicant has any record of any "problems", it gets denied.
After about 6 months, you get the CCW permit.
Note: this does not apply to New York City, where very few can get a permit.