Downing Street Playground[1] is on 6th Avenue between Carmine Street and Downing Street in Greenwich Village, Manhattan. It was built by the WPA in 1935, opening on May 29th of that year. Today it is coupled with Winston Churchill Square[2], a small garden and sitting area that was added in 1943. It's not clear if the latter can be counted as a New Deal site —it depends on exactly when the work was done and who paid for it. But the rest of Downing Street playground was built in 1935 along with many others, as indicated in the Parks Department press release[3]:

The schedule of 160 new playgrounds announced by the Park Department on January 1st of this year has been increased by forty-three new areas, making a total to be completed by next summer of 203 new recreational units. Seventy-three of these play areas have already been opened to the public. Seventy of these were constructed with city, state and federal relief funds by the Park Department and three of them were developed by the Long Island State Park Commission and the New York State Department of Public Works in conjunction with the construction of the Grand Central Parkway through Alley Pond and Hillside Parks in the Borough of Queens. The following is a list with the dates on which these facilities were opened:

A long list follows, which includes:

May 29   A   Manhattan   Downing & Carmine Streets

1. Downing Street Playground - History, NYC Department of Parks website (fails to mention New Deal assistance).
2. Downing Street Playground - Sir Winston Churchill Square, NYC Department of Parks website.
3. NYC Department of Parks Press Release, August 12, 1935.