We present the derivation and implementation of complex, frequency-dependent polarizabilities for excited states using the algebraic-diagrammatic construction for the polarization propagator (ADC) and its intermediate state representation. Based on the complex polarizability, we evaluate C-6 dispersion coefficients for excited states. The methodology is implemented up to third order in perturbation theory in the Python-driven adcc toolkit for the development and application of ADC methods. We exemplify the approach using illustrative model systems and compare it to results from other ab initio methods and from experiments.