  We perform long-term simulations, up to ten billion years, of closely-spaced
configurations of 2 -- 6 planets, each as massive as the Earth, traveling on
nested orbits about either stellar component in $\alpha$ Centauri AB. The
innermost planet initially orbits at either the inner edge of its star's
empirical habitable zone (HZ) or the inner edge of its star's conservative HZ.
Although individual planets on low inclination, low eccentricity, orbits can
survive throughout the habitable zones of both stars, perturbations from the
companion star require that the minimum spacing of planets in multi-planet
systems within the habitable zones of each star must be significantly larger
than the spacing of similar multi-planet systems orbiting single stars in order
to be long-lived. The binary companion induces a forced eccentricity upon the
orbits of planets in orbit around either star. Planets on appropriately-phased
circumstellar orbits with initial eccentricities equal to their forced
eccentricities can survive on more closely spaced orbits than those with
initially circular orbits, although the required spacing remains higher than
for planets orbiting single stars. A total of up to nine planets on nested
prograde orbits can survive for the current age of the system within the
empirical HZs of the two stars, with five of these orbiting $\alpha$ Centauri B
and four orbiting $\alpha$ Centauri A.
