I saw the Coyote for only a few minutes on Thursday evening while the weather switched between snow and rain. The Coyote certainly does not like being near people. If it sees you looking in its direction, it instantly moves away. This bodes well for the Coyote. If it can stay out of people's way, there should be no need to remove it from the park.
I'm always surprised when people don't expect there to be nature in New York City. Given the expansion of Coyotes in the eastern United States, it was only a mater of time before we got another one wandering into Central Park.
If I look at my ancestors in America, they started as rural farmers, then moved to towns and then cities. (Ironically my first ancestors, which date back from the 1640s, were from what is now Brooklyn.) The towns protected them from wild animals and as they moved to cities there was this added artificial concept of a "man-made world", separate from the natural world.
The natural world never really left, but an illusion was created that nature had been tamed, as though somehow animals were as controlled as the city's landscaped gardens.
When we have a Red-tailed Nest (the Trump Parc nest was only 300 yards from the Coyote), a Wild Turkey or a Great Horned Owl in the city, it makes news. While the wild animals captivate us, what really seems to excite us is the realization that despite our best efforts to create a "man-made world", we're still really living in the "natural world".