The bronze statue, by Milton Hebal, still stands outside the Delacorte Theater. The payphones, seen here in March, 2012, didn’t make it.

Even when this photo was taken in March, 2012, the phones were dead. Verizon exited the payphone business in 2010 and did a pretty sorry job of cleaning up after itself. For years about a dozen of these dormant telephonic carcasses stubbornly lingered.
Today a few Verizon payphones remain across Central Park, indoors and out. The last Central Park payphone that had dial tone, by the Kerbs Boathouse, finally kicked it a couple of years ago but as far as I know the phone itself still hangs on the wall.
I would not know when these phones at the Delacorte Theater disappeared but their former numbers remain out of service:
(212) 650-1805
(212) 650-9396
(212) 650-1388