Currently there are 19 native SuperZoom lenses for Sony A77 II and all of these lenses are autofocus (AF) type.
A77 II also has a sensor based image stabilization system which means that all of these lenses will be stabilized when used on A77 II.
Since Sony A77 II has environmental sealings (Weather Sealing), you may like to couple your camera with one of these 2 SuperZoom lenses with Weather Sealings.