Situation: Radio Shack wall transformer with 11 VDC unregulated output is
going into an LM371. I want to shunt with a pair of 5.1 V , 1A Zeners in
series
so that my adjustable output voltage is repeatable. Presently my Zener
series resistor is 180 ohms.

Problem.. I'm frying my zeners!!

What should I be doing differently?

Are you sure the zeners are in the correct polarity ? Also I have not
looked at the way zeners are speced lately but aren't they specified as
Watts instead of Amps ?