Currently there are 45 native Telephoto Zoom lenses for Nikon D600 and all of these lenses are autofocus (AF) type.
Nikon D600 doesn't have a sensor based image stabilization system but 33 of these Telephoto Zoom lenses features optical image stabilization.
Since Nikon D600 has environmental sealings (Weather Sealing), you may like to couple your camera with one of these 19 Telephoto Zoom lenses with Weather Sealings.