I think you mean longitudinal stability?
An airplanes longitudinal stability depends on the relative position between the CG and the wing and fuselage aerodynamic center, on the one hand, and on the tail plane effect, on the other. GG behind AC: wing-fuselage unstable. CG ahead AC: wing-fuselage stable. The tailplane is always stabilizing, no matter what is its angle of incidence. The sum of both effects determines overall longitudinal stability.
If the tailplane is powerful enough, its stabilizing effect can make stable an airplane with a CG such that it has an unstable wing-fuselage. I think that is the case in most airliners.
The tailplane, however, has another function. To make it possible for the airplane to be in trim (ANU moments=AND moments). Then we have to look at the center of pressures, instead of the AC. If the CG is behind the CP, that is an ANU moment. If the CG is ahead, that is a AND moment. The aerodynamic moment is always ANU, I think.
In flight, I think that the CP can either be ahead or behind the CG, depending on the CG location and the AoA. So the tailplane will either produce an AND or an ANU moment to balance all the moments and make the airplane fly in trim.
It is true that on most occasions, the tailplane produces a downwards force, but sometimes can produce an upwards one (the ideal case for cruise).