I've never heard of any caliber restrictions as long as its a centerfire cartridge.
It is unlawful to hunt big game with:
* A firearm or bow aided by any artificial light or a laser that projects a beam toward the target.
* An autoloading firearm with a capacity of more than 6 shells (one which requires that the trigger be pulled separately for each shot), except an autoloading pistol with a barrel length of less than 8 inches.
* A firearm using rimfire ammunition.
* A shotgun of less than 20 gauge or any shotgun loaded with shells other than those carrying a single projectile.
* A bow with a draw weight of 35 lbs or less.
* Arrows with barbed broadheads; arrowheads less than 7/8 inches at the widest point or with less than 2 sharp cutting edges.
* Dogs.
* Aircraft of any kind.
* Bait.
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 nonbarbed, 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
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:
* 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.
www.dec.state.ny.us/website/dfwmr/wildlife/guide/biggame.html#Manner