excerpted quotes from New York State DEC website

Manner of Taking
[url]http://www.dec.state.ny.us/website/dfwmr/wildlife/guide/hunting.html#Possession[/url]
It is illegal to take or hunt wildlife:
-with any firearm equipped with a silencer.
-with any firearm which continues to fire as long as the trigger is held back (an automatic firearm).
-with any semi-automatic firearm with a capacity to hold more than 6 rounds, except firearms using .22 or .17 caliber rimfire ammunition, firearms altered to reduce their capacity to no more than 6 shells at one time in the magazine and chamber combined, or autoloading pistols with a barrel length of less than eight inches....

Prohibitions (for hunting Migratory Gamebirds)
[url]http://www.dec.state.ny.us/website/dfwmr/wildlife/guide/migbregs.html[/url]
You may NOT hunt migratory game birds using these methods:
-With a shotgun that holds more than three shells, unless it has a plug that cannot be removed without taking the shotgun apart.
-With a shotgun larger than 10 gauge, or with a rifle or handgun.
-With a swivel gun, battery gun, machine gun, or explosive.

Special regs for LawnGuyLand (Long Island, Suffolk county)
[url]http://www.dec.state.ny.us/website/dfwmr/wma/smland.htm[/url]
Manner of Taking: Shotgun, using a single ball or slug, or a muzzleloading rifle, shooting a single projectile, having a minimum bore of .44 inches. Shotgun barrels may be rifled, and telescopic sights may be used. No muzzleloading pistols are permitted...

[url]http://www.dec.state.ny.us/website/dfwmr/wildlife/guide/smallgame.html#Furbearer[/url]

In New York State, nearly all species of wildlife are protected. Most species, including endangered species, songbirds, hawks and owls are fully protected and may not be taken. The few unprotected species include porcupine, red squirrel, woodchuck, English sparrow, starling, wild pigeon, monk parakeet and snapping turtle. Unprotected species may be taken at any time without limit. A hunting license is required to hunt unprotected wildlife with a bow or firearm
...
Furbearer Hunting:
To hunt furbearers, you need to possess a junior hunting, small game hunting, sportsman, nonresident hunting, or nonresident combination license. A trapping or big game license does not allow you to hunt furbearers. All laws pertaining to the use of a spotlight and firearm apply.

You may hunt red and gray fox, coyote, bobcat, raccoon, skunk, mink, weasel and opossum.
-If you take a coyote or bobcat, it must be tagged and sealed .
-You may use a call, including an electronic call.
-You may hunt furbearers only after sunrise on the opening day. They may be taken at any hour, day or night, for the rest of their hunting season.
-Skunk may be hunted during their open trapping season.
-Mink may be hunted in the Southern Zone with a .22 caliber firearm during their open trapping season. Mink may not be hunted with a firearm in the Northern Zone
-Muskrat may only be hunted on Lake Champlain during the open trapping seasonwith a firearm not larger than a .22 caliber.
-You may hunt furbearers during the day using any handgun, shotgun or rifle. You may hunt at night as described below:

Furbearer Hunting at Night
You may hunt furbearers at night, with or without a light, as follows:

-Use any handgun.
-Use a shotgun loaded with shot (any size).
-Use a rifle chambered in any cartridge, except that you may not possess a centerfire rifle afield, during the day or night, during any open season for deer in areas restricted to using a shotgun only for deer.

[b][red]If hunting without a light, the use of a light gathering ("starlight") scope is legal on any firearm listed above.[/b][/red]

Quoted:
10 rounds max in every state? Either that's wrong, or I've been hunting with 20 more than I should be.