Stability with respect to what? voltage supplies, time (long term drift), temperature. . . I would just believe the manufacturers spec. or if in doubt buy a much better one!
Frank
I suppose, you are referring to the dynamic stability properties determined by negative feedback, correct?
Measurement is rather simple: Apply feedback as desired and verify if the output is fixed at a certain (desired) dc voltage without any oscillation.
A quick time-domain check is to input a low voltage square-wave signal to the closed-loop circuit. The amount of overshoot/ringing on the rising and falling edges is a measure of the stability. A properly stabilized circuit will have little or no overshoot/ringing.
Make your opamp as a closed loop by connecting a probe which connects the output and input(in1 or in2 based on your circuit). Then run the stability analysis by considering the probe as a stability finder. Check stability summary if phase margin is 60 to 90deg means your circuit has good stability which avoid osscilation and less ringingggggggg