What measurement can be used to determine the stability of the atmosphere?

I would say pressure, but it might depend on what you mean by stability. Pressure will tell you how many particles and how energized those particles are, the more particles the higher the pressure, the harder it is to change or remove the atmosphere due to the larger mass of it. Also consistent pressure measurements can tell you how stable the atmosphere in a particular region is. So if stability means how consistent are the weather conditions, pressure can be a good indicator too, differences and changing pressures can cause weather catastrophes like tornados and hurricanes.