Are you sure it's the tail piece itsself? Could it be that one of the fine tuners is touching the belly? That will cause buzz. If that is it, loosen the string, readjust the tuner so it is NOT touching, then re tune with peg.

Or, it could possibly be that the gut holding the tailpiece to the end pin is too loose....if that is the case, take it to a luthier. I don't know how to fix that.