The Bedford-Stuyvesant neighborhood of Brooklyn was called “‘Little Harlem’ of Brooklyn” in the 1938 Brooklyn (NY) Daily Eagle and “Brooklyn’s ‘Little Harlem’” in the 1943 New York (NY) Times. Both Bedford-Stuyvesant and Harlem have large African-American populations. The “Little Harlem” nickname has been only infrequently used.
 
“Little Harlem” is also a nickname for Corona, Queens.
       
 
Wikipedia: Bedford-Stuyvesant, Brooklyn
Bedford–Stuyvesant (/ˈbɛdfərdˈstaɪvəsənt/; colloquially known as Bed–Stuy and occasionally Stuyford) is a neighborhood of 153,000 inhabitants in the north central portion of the New York City borough of Brooklyn. The neighborhood is part of Brooklyn Community Board 3, Brooklyn Community Board 8, and Brooklyn Community Board 16. The neighborhood is patrolled by the NYPD’s 79th and 81st precincts. In the City Council, the district is represented by Robert Cornegy of the 36th Council District.
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1960s
Gang wars erupted in 1961 in Bedford–Stuyvesant. During the same year, Alfred E. Clark of The New York Times referred to it as “Brooklyn’s Little Harlem”.
 
Old Fulton NY Post Cards
29 June 1938, Brooklyn (NY) Daily Eagle, pg. 15, col. 2:
Our Negro Neighbors
The Bedford-Stuyvesant District Is Termed ‘Little Harlem’ of Brooklyn—A Negro Community Built With WPA Funds Is Suggested
LITTLE HARLEM, and a suburb to Harlem, ardent civic leaders have termed the Bedford-Stuyvesant district, Brooklyn’s largest colored colony in the heart of a once fine neighborhood.
 
16 November 1943, New York (NY) Times, pg. 1, col. 1:
MAYOR DENOUNCED BY JURY FOR CRIME IN BROOKLYN AREA
Accused of ‘Assisting’ Lawless Elements in the Bedford-Stuyvesant ‘Little Harlem’
REIGN OF TERROR ALLEGED
Big Increase in Police Guard Among 11 Recommendations for Restoring Order
A Kings County grand jury denounced Mayor La Guardia yesterday for his failure to curb lawlessness in Brooklyn’s “Little Harlem,” the Bedford-Stuyvesant area, and also took the Mayor to task for broadcasting over the municipal station, WNYC, that those who had complained about these conditions were “crackpots” and “publicity seekers.”
 
Old Fulton NY Post Cards
1 May 1958, New York (NY) Post, pg. 10, col. 1:
INSIDE BEDFORD-STUYVESANT
Bedford-Stuyvesant is an area of approximately five square miles in the borough of Brooklyn.
 
It’s called Brooklyn’s “Little Harlem” because its 200,000 Negroes outnumber the white inhabitants four to one—and the ratio keeps growing bigger all the time.
 
New York (NY) Times
GANG WARS UPSET AREA IN BROOKLYN; Bedford - Stuyvesant Tense Following Two Slayings
By ALFRED E. CLARK
May 02, 1961
Page 31
Tension grips Bedford-Stuyvesant—Brooklyn’s Little Harlem—in the aftermath of last week’s street-gang warfare that took the lives of two teenagers.
 
Google Books
The Other Americans:
How Immigrants Renew Our Country, Our Economy, and Our Values
By Joel Millman
New York, NY: Viking
1997
Pg. 69:
West Indians flocked to Bedford-Stuyvesant, Brooklyn’s “Little Harlem.”
 
Twitter
Maya Wiley
‏@mayawiley
@BKMovement Bed-Stuy is little Harlem and people civiclly active and engaged.
12:33 PM - 4 Oct 2012
       
Twitter
BrownstoneDetectives
‏@BrownstoneDetec BrownstoneDetectives Retweeted The Bowery Boys NYC
Everyone used to always compare Brooklyn to Harlem, didn’t they! Bed-Stuy was once “Little Harlem”!BrownstoneDetectives added,
The Bowery Boys NYC @BoweryBoys
Where did Ozone Park get its unusual name? And why was it called the “Harlem of Brooklyn”? http://bit.ly/1Upn04Z 
1:54 PM - 1 Sep 2015
 
Twitter
Is Vin Diesel Black?
‏@StevenWoberts
No one calls Bed Stuy “Little Harlem.” I will punch anyone who says that phrase.
4:42 PM - 7 Nov 2016
 
Forbes
NOV 26, 2016 @ 02:48 PM
The Quietly Radical, 60-Year-Old Signs of Bed-Stuy
David Alm ,  CONTRIBUTOR
(...)
The signs represent the effort of more than 100 block associations that formed as early as the 1930s to fight white-supremacist groups attempting to keep blacks out of Bed-Stuy. Among the more prominent of these groups was the Midtown Civic League, which formed in the late 1930s when large numbers of African Americans were migrating from Harlem, in Upper Manhattan, to Bed-Stuy, earning the neighborhood the nickname of “Brooklyn’s Little Harlem.”