No. If you and the seller are not both NYS residents then it violates the 1968 Gun Control Act to sell the gun to him/her.
However, you can contact an FFL and pay them a fee (e.g. $25) to log the gun into their inventory and then transfer it to the buyer. So long as the buyer is a resident of a state that allows out-of-state purchases (and most do, but not NJ and CA, among others) and passes the background check it's not a big deal at all. Don't get scammed into paying sales tax to the dealer -- you are paying for a transfer of possession, not title.