What type of visa do you have? I am a Canadian with a G4 vvisa and have a suffolk county pistol license. My suggestion is to call the licensing department and ask them. I did, then they asked that I send a letter explaining my situation (visa, etc,,,) they went up the line to find out if I was allowed. It turns out I was and then I went through the process. It helps if you have a NY driving license and a social security number. At the end of the day it was a lot of red tape but still easier than getting one in Canada.
If you decide to buy go to Suffolk Sportsman, Al helped me out there a lot ... it was tricky but he knows what to do.
Send me an e-mail if you want to talk offline about it.