I personally believe that the second amendment should apply only to American citizens.
This issue goes all the way back to the Dred Scott case in 1857 where Chief Justice Roger B. Taney ruled that any person descended from Africans, whether slave or free, is not a citizen of the United States. The ruling stated that if African Americans were to be granted citizenship then the constitution would apply, allowing them to speak freely, go where they liked unmolested and bear arms. This decision was later overturned. Dred Scott, his wife and daughters were formally freed by Henry Taylor Blow on May 26, 1857, less than three months after the Supreme Court decision by Chief Justice Roger Taney.
The ruling of the court helped catalyze sentiment for Abraham Lincoln's Emancipation Proclamation and the three constitutional amendments ratified shortly after the Civil War: the Thirteenth, Fourteenth and Fifteenth amendments, abolishing slavery, granting former slaves citizenship, and conferring citizenship to anyone born in the United States.
Surprisingly, NY will issue a CCW permit to a resident alien.