The New York City Park Department Report to August 1934[1] states on Page 18:

FORT TRYON PARK IN MANHATTAN This park was purchased by John D. Rockefeller, at a cost of $1,500,000. The contract between Mr. Rockefeller and the City provided that the donor of the property should do most of the construction vork. This has been completed at a cost of $4,000,000. The City is obligated to complete approximately $600,000. worth of work, consisting mainly of roads, paths, drainage systems, sewer systems, and park lighting. $300,000. worth of this work has been done with Work Relief labor and with an appropriation of $150,000. by the Board of Estimate and Apportionment during the year 1934. The park cannot be opened until funds for the balance of the work amounting to $300,000. have been made available.

Probably meaning that $150,000 was paid by the CWA, TERA, or similar federal agency, and the City had to find the rest somewhere else. What happened after that I don't know. Meanwhile The Cloisters Museum of medieval art is in Fort Tryon Park, and this, too was always assumed to be a 100-percent Rockefeller-funded creation, but I just came upon a book[5] that says:

During the Great Depression of the 1930s, when many architects, sculptors and painters were on emergency relief, [James J.] Rorimer seized on the idea of using them to make a study model of the proposed museum (Fig.12), with sculpture and frescoes to scale and the light coming through the windws the way it would if it were built.[28] When he showed it to Rockefeller, who looked at it intently and asked: "Is this the way The Cloisters is going to look?," Rorimer replied: "No, Mr. Rockefeller, it is not the way it is going to look. It is merely the way it could look if you wanted it to." Rorimer always maintained that Rockefeller's reaction to his reply kindled his enthusiasm for continuing the work. To do so at that time must have taken a good deal of courage in the face of almost certain criticism: that so wealthy a man should spend so much money in such a way when so many were suffering. But Rockefeller was thinking of the public good in the years to come.

Footnote

18. The study model was made by the Museum's Department of Medieval Art with the cooperation of the Architects' Emergency Committee (later Emergency Relief Bureau) [The Metropolitan Museum of Art Sixty-Sixth Annual Report of the Trustees 1935, p.29.

(Click on the last thumbnail above to see the Cloister mockup.) This implies New Deal labor (I imagine one of the purposes of the Architects' Emergency Committee was to find gigs for unemployed architects who would be paid by a New Deal agency; this is semi-confirmed in [8]). In any case, I found a Roosevelt (Eleanor) connection HERE.

While looking for information on the Architects' Emergency Committee, I also came upon the following tidbit about Bryant Park:

...its scope is of enexpected interest in that it technically wraps around the [New York Public] library and extends to 5th Avenue itself to include the entrance terrace to the library ... [I]n 1933 during the Depression, the Architects' Emergency Committee held a competition — limited to unemployed architects and draftsmen — for its rejuvenation. This was won by Lusby Simpson, and the landscaping and planting was carried out in in 1934 by the Parks Department under its new commissioner Robert Moses, with Aymar Embury, Jr., architect to the department.[6]

Obviously the landscaping and planting work would have been done by relief workers. And perhaps not so obviously, Embury was the top architect at the New Deal era Parks Department and he was on the federal payroll. Moses himself hints at the scope of the project in his 1938 progress report:

New construction in old parks has produced such facilities as tho new zoos in Central and Prospect Parks and in Barrett Park, Staten Island, the improvement of the lower reservoir site in Central Park, the entire reconstruction of Bryant Park and Stuyvesant Park, and hundreds of lesser projects.

See this page for the story of New Deal work on Bryant Park. I also found a NY Times obituary for Julian Clarence Levi[7], who founded the Architects' Emergency Committee, which "found 7400 jobs for architects". Strangely enough on the facing page of the same issue, I see the obituary of Columbia Professor Wallace Eckert, a pioneer in computing about whom I have done a fair amount of research (not New-Deal related as far as I know).

1. Park Department Report to August 1934, NYC records archive, accessed March 7, 2018.
2. Fort Tryon Park, NYC Parks Department website, accessed March 8, 2018.
3. Fort Tryon Park History, NYC Parks Department website, accessed March 8, 2018.
4. Fort Tryon Park, Wikipedia, accessed March 8, 2018.
5. The Cloisters: Studies in Honor of the Fiftieth Anniversary, The Metropolitan Museum of Art (1992), p.58.
6. G.E. Kidder Smith, Source Book of American Architecture: 500 Notable Buildings from the 10th Century to the Present, Princeton Architectural Press (2000), p.321.
7. Johnston, Laurie, "Julian Clarence Levi Dies at 96; Oldest Alumnus of Columbia U, New York Times, 25 August 1971, p.40.
8. Schwartz, Bonnie Fox, The Civil Works Administration, 1933-1934, Princeton University Press (1984), p.141: "The New York State Employment Service director had previously cooperated with the Architects Emergency Committee [and some others] under the Temporary Emergency Relief Administration, and this practice continued under the CWA."