Can you put a supercharger on a Automatic and will It mess up the engine or
 

transmission? It's a D16Y8 Engine

It's a "Honda", 2.0 liters is a bottle of soda, not an engine.

i think depends on hp!

Sometimes auto trannies are actually better for crap liek this because auto trannies almost always have a trans cooler and much more tranny oil but and this is a big one, auto transmissions are severely more difficult and expensive to repair then manual transmissions. If I were you I would worry more about the cost of actually adding a supercharger then the problems you would have with it, You are going to spend at the very least 1300 just on the hardware alone and if you do it yourself there is a extremely small margin of error not to mention a very long list of other mods that need to be done to make a supercharger or turbocharger effective such as ECM programming and sometimes the inefitable swap to MAP as opposed to MAF.