Hi Brian Not sure if the Zenith carb is the same wherever you are as it would be here in the UK, where it is, or at least was, a popular carb found in many cars, sometimes also known as the Stromberg CD and sometimes mistaken for the SU, both of which are on many aero VW engines. Both can be identified by the black plastic knob about 1/2" across at the top of the suction housing which unscrews with the fingers. If it is this one, you sound to have a common problem with these carbs which is either connected with a leaking diaphragm, or incorrect oil or oil level in the dashpot. I can give more details about the carb and how to hopefully cure the problem if it sounds like the same model.
Regards Phil