Currently there are 13 native Telephoto Prime lenses for Sony A77 and 9 of these lenses are autofocus (AF) type.
A77 also has a sensor based image stabilization system which means that all of these lenses will be stabilized when used on A77.
Since Sony A77 has environmental sealings (Weather Sealing), you may like to couple your camera with one of these 2 Telephoto Prime lenses with Weather Sealings.