“Bone Alley” used to be a densely populated and filthy area of Manhattan, at Pitt Street and Willett Street. The New-York (NY) Daily Tribune of May 12, 1875 probably explains the name:
 
“There are six tenements situated in the rear of Nos. 115, 117, 119, 199 1/2, 121, and 123 Willett st., that are approached through an alley-way, Bone-alley. Joseph Graf and Mrs. Mary Steve are there engaged in the business of scraping decayed meat from old bones which have been picked up by rag-pickers in different parts of the city. In the rear yard of this house is a wooden shed, where the bones are piled up as they are purchased from the rag-pickers. The work caused a very offensive odor.”
 
Bone Alley was destroyed in the 1890s and replaced with the current Hamilton Fish Park.
   
 
Wikipedia: Bone Alley
Bone Alley was a city block of New York City bounded by Houston Street, Willett Street, Stanton Street, and Pitt Street. In 1897 the block contained sixty-three houses, three hundred and sixty-three families, and one thousand six hundred and fifty people. The death rate on the block of Bone Alley was 26.06%, while the death rate in the alley itself was 47.97%.
 
The locale was filthy. Located in New Israel, Bone Alley was known as the most crowded place on earth. A park was planned to replace it by the last years of the 19th century. Its population consisted of Italians, Poles, Germans, Hungarians, and Russians.
 
Bone Alley was razed to make room for Hamilton Fish Park, which was constructed from 1896 - 1898. It was located south of Houston Street, between Pitt Street and Sheriff Street. The park consisted of a playground with a gymnasium and a kindergarten. There was also an expanse of green lawns, benches, and a rest house containing baths.
 
23 July 1874, New York (NY) Herald, pg. 11, col. 1:
BONE ALLEY.
THE HOME OF THE RAG PICKERS
Where Rags, Bones, Fat and Bottles Go.
From Cellar to Roof—Down in the Depths—The Toilers in Dust and Mire.
Among the poor quarters of the city none are poorer than that which borders the Easr River, from James slip to the foot of Houston street. This district includes, in its two extremes, the wretched cellars of Water street, with their accompaniment of bucket shops, velvet rooms and “sailors decoy” dens, and the reeking tenements of Cherry, Pitt, Willett and Goerek streets. The northern portion of this squalid region is, in a great part, the home of the rag pickers, and lies Bone alley.
 
Chronicling America
12 May 1875, New-York (NY) Daily Tribune, “City Sanitary Measures,” pg. 12, col. 1:
There are six tenements situated in the rear of Nos. 115, 117, 119, 199 1/2, 121, and 123 Willett st., that are approached through an alley-way, Bone-alley. Joseph Graf and Mrs. Mary Steve are there engaged in the business of scraping decayed meat from old bones which have been picked up by rag-pickers in different parts of the city. In the rear yard of this house is a wooden shed, where the bones are piled up as they are purchased from the rag-pickers. The work caused a very offensive odor. Graf and Mrs. Steve were arrested, and committed on default of $100 on charge of violations of sections 79 and 80 of the Sanitary Code.
 
Chronicling America
14 March 1896, New-York (NY) Daily Tribune, “For a Small Park in Sheriff St.,” pg. 13, col. 3:
The Rev. John B. Devins, a member of the sub-committee to which the question of the site was referred, reported for the majority of the commission in favor of the Sheriff-st. site, urging that it was the most populous district in the world and included Bone Alley, on the of the city’s eyesores and nuisances.
 
Chronicling America
29 March 1896, New-York (NY) Daily Tribune, pg. 25, col. 4:
BONE ALLEY UNDER THE BAN
IT WILL PROBABLY MAKE WAY FOR A SMALL PARK
 
Chronicling America
7 June 1896, New-York (NY) Daily Tribune, pg. 15, col. 1:
SORRY TO QUIT BONE ALLEY.
MARTIN SHREINER HAS LIVED IN THE BLOCK SIXTY-TWO YEARS.
       
Google Books
8 December 1898, The Nation, pg. 480, col. 2:
Cat Alley was one of the “slum alleys” of New York swept away by sanitary reform, together with Bottle Alley, Bandits’ Roost, Bone Alley, Nipsey’s Alley, and Gotham Court. The description of these alleys and other slums, such as “Hell’s Kitchen” (which still persists), feebly recalls the old New York of 1850, when Five Points was in its heyday.
 
Museum of the City of New York 
Jacob A. (Jacob August) Riis (1849-1914)
Bone Alley Park site—when the tenements were torn down, one of the small park sites I [Jacob A. Riis] located, taken 1898.
DATE:1898
The cleared blocks of land to become Bone Alley Park.
 
Google Books
May 1899, The Atlantic Monthly, “The Battle with the Slum” by Jacob A. Riis, pg. 631:
We bought the slum off in the Mulberry Bend at its own figure. On the rear tenements we set the price, and it was low. It was a long step. Bottle Alley is gone, and Bandits’ Roost. Bone Alley, Thieves’ Alley, and Kerosene Row, — they are all gone. Hell’s Kitchen and Poverty Gap have acquired standards of decency; Poverty Gap has risen even to the height of neckties.
 
Google Books
The Battle with the Slum
By Jacob A. Riis
New York, NY: The Macmillan Company
1902
Pg. 285:
To return to the East Side where the light was let in. Bone Alley brought thirty-seven dollars under the auctioneer’s hammer. Thieves’ Alley, in the other park down at Rutgers Square, where hte police clubbed the Jewish cloakmakers a few years ago for the offence of gathering to assert their right to “being men, live the life of men,” as some one who knew summed up the labor movement, brought only seven dollars, and the old Helvetia House, where Boss Tweed and gang met at night to plan their plundering raids on the city’s treasury, was knocked down for five. Kerosene Row, on the same block, did not bring enough to have bought kindling wood with which to start one of the (Pg. 286—ed.) numerous fires that gave it its bad name. It was in Thieves’ Alley that the owner in the days long gone by hung out the sign, “No Jews need apply.” I stood and watched the opening of the first municipal playground upon the site of the old alley, and in the thousands that thronged street and tenements from curb to roof with thunder of applause, there were not twoscore who could have found lodging with the old Jew-baiter. He had to go with his alley, before the better day could bring light and hope to the Tenth Ward.
 
Google Books
Men Along the Shore
By Maud Russell
New York, NY: Brussel & Brussel
1966
Pg. 97:
The colorful, if unflattering, names of slum streets — Bottle Alley, Bone Alley, Bandits’ Roost, Thieves’ Alley, Kerosene Row — were being given more sedate and probably less accurate titles.