Currently there are 2 native SuperZoom lenses for Sony A7c and all of these lenses are autofocus (AF) type.
A7c also has a sensor based image stabilization system which means that all of these lenses will be stabilized when used on A7c.
Since Sony A7c has environmental sealings (Weather Sealing), you may like to couple your camera with one of these 1 SuperZoom lenses with Weather Sealings.