You enter Billy Johnson Playground (mid Central Park at 67th Street) through a leafy bower; there is the usual swing set, a large sand box, and a couple of picnic tables surrounded by benches. And then, carved into the side of an immense rock, teensy steps to help children negotiate their way up to a slide at the summit. The intoxicating sense of fear felt sliding down a curved 20-foot trough in the rock can be intensified, according to playground rumor, by riding aboard a custom cut-out piece of corrugated cardboard.