Binary stars are universally thought as second rate sites for the location of habitable planets. It is still open to debate, in current planet-forming theory, whether planetary formation similar to that of single stars can proceed in multiple systems, and whether, once formed, these planets have a substantial probability of remaining in stable orbits inside the stellar continuously habitable zones (CHZs) for lengths of time compatible with the evolution of life. Here we consider binary stars having masses, ages and luminosities compatible with the long term permanence of habitable telluric planets inside their CHZ. We investigate the dynamical stability of the system composed by the binary and an Earth-like planet within the CHZ of the primary and secondary component: Centauri was chosen as the main study case. We obtain the boundaries of the system's secular stability as a function of mass, semi-Major axis and inclination. We conclude that stable planetary orbits do exist in the CHZs of these stars, but for those systems with periods similar to or less than 100 years, short-period perturbations lead to oscillations in the planetary semi-major axis up to 100 times larger than those suffered by Earth's orbit. This might be of consequence for the long term planetary climate stability and the periodical onset of ice ages.
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