There actually is a NY non-resident permit, but in order to get it, your principal job or the principal location of your business has to be in New York. The local constabulary that taught me the required safety class to get my permit did not know this, and tried to embarrass me in front of the class, but they had not read Section 400 Para. 3 of the NYS Penal Code which covers this and reads in part: "Applications shall be made and renewed, in the case of a license to carry or possess a pistol or revolver, to the licensing officer in the city or county, as the case may be, where the applicant resides, is principally employed, or has his principal place of business as merchant or storekeeper..."
Further proof that this actually exists came to the front when a Westchester newspaper was sued for publishing the names and addresses of all pistol permits the county had recently issued. This list included people living in CT, VA, FL, and several other states (I believe OH was one, but I'm not sure of that). Obviously, these were folk who either worked principally in NY or had businesses in NY. The suit, by the way, embarrassed Westchester, and now anyone applying for a permit in NY can sign an exemption form that prohibits anyone from publishing him/her as a CHP owner.