"Little Jamaica" is used infrequently, although New York City has many immigrants from Jamaica. "Little Kingston" (after Kingston, Jamaica's capital city) is even less frequently used.

http://en.wikipedia.org/wiki/Jamaica
New York City is home to the largest Jamaican diaspora of all, with a large community along Flatbush avenue in Brooklyn—centered around the neighborhoods of Prospect Heights, Prospect Lefferts Gardens and Flatbush. The Bronx also has a significant Jamaican ex-pat community. Flatbush Avenue features several miles of Jamaican cuisine, markets, nightlife and residential enclaves.

http://www.citylimits.org/content/articles/articleView.cfm?articlenumber=991
I grew up in "Little Jamaica," a West Indian neighborhood in the Bronx's northeast section. I was a sheltered bookworm, unaware of much of the drama that lurked around my own corner--save for the occasional boom of bullets at midnight.

http://www.mbroder.com/blogs/index.php/2005/03/
A realtor who didn't show for a house viewing because he didn't think I was serious about living in what he so condescendingly refers to as "Little Jamaica" (aka Crown Heights);
http://talesmag.com/tales/road/jamaica_no_problem.shtml
In New York, I lived just blocks from the area in Brooklyn known as "Little Kingston," so I was familiar with their ways and had friends who were from "J," as they referred to the island.

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