We present a theoretical study of the polarizabilities of free and disubstituted azoarenes employing auxiliary density perturbation theory (ADPT) and the noniterative approximation to the coupled perturbed Kohn-Sham (NIA-CPKS) method. Both methods are noniterative but use different approaches to obtain the perturbed density matrix. NIA-CPKS is different froth the conventional CPKS approach in that the perturbed Kohn-Sham matrix is obtained numerically, thereby yielding a single-step solution to CPKS. ADPT is an alternative approach to the analytical CPKS method in the framework of the auxiliary density functional theory. It is shown that the polarizabilities obtained using these two methods are in good agreement with each other. Comparisons are made for disubstituted azoarenes, which give support to the push-pull mechanism. Both methods reproduce the same trend for polarizabilities because of the substitution pattern of the azoarene moiety. Our results are consistent with the standard organic chemistry ``activating/deactivating'' sequence. We present the polarizabilities of the above molecules calculated with three different exchange-correlation functionals and two different auxiliary function sets. The computational advantages of both methods are also discussed.