I don't think you can use buckshot in New York. I could be wrong, but this is from their website.
Descriptions of Legal Implements for Big Game Hunting
Bow-
Long (stick), recurve or compound bow with a draw weight in excess of 35 pounds. A legal arrowhead is non-barbed, has 2 or more cutting edges and is at least 7/8 inches wide.
Muzzleloader-
Firearm loaded through the muzzle, a minimum bore of .44 inches and shooting a single projectile. Scopes may now be used during the Special Muzzleloading Season in addition to the Regular Big Game Season and the Early Bear Season. See
Muzzleloading section of regulations for special requirements during the muzzleloading season.
Handgun*-
any centerfire pistol or revolver. Barrel length maximum is 16 inches
(NOTE: Possession of handguns in New York State requires a NYS Pistol Permit. New York does not recognize permits issued by other states.)
Shotgun*-
Must be 20 gauge of larger and fire a single projectile, rifling in the barrel or choke is allowed
Rifle* -
any centerfire rifle.
* - It is illegal to hunt with:
[ul][*]a fully automatic firearm;[*]an autoloading firearm that holds more than 6 shells (except an autoloading pistol with a barrel length under 8 inches);[*]any firearm equipped with a silencer. [/ul]