Little Ireland? That's not a neighborhood -- that's New York City! "'Little Ireland,' sometimes known as the city of New-York" was cited in print in 1891.

The Bronx neighborhood of Woodlawn has also been called a "Little Ireland."


21 January 1891, New York (NY) Times, pg. 5:
To the Editor of the New-York Times:
(...)
At one time there was serious thought on the part of Messrs. Sheehan and Murphy, speaking for the interior of the State, and of Messrs. McLaughlin, Grant, Gilroy, and Martin, speaking for Brooklyn and "Little Ireland," sometimes known as the city of New-York, of presenting the Senatorship to Parnell.
(...)
A CITIZEN OF "LITTLE IRELAND."

24 January 1891, New York (NY) Times, pg. 5:
To the Editor of the New-York Times:
(...)
The second purpose of these municipal reformers, it is whispered, is the change of name - New-York to New-Cork. This is shorter, less violent, and more pleasing to our rulers than "Little Ireland."
(...)
A CITIZEN OF NEW-CORK.