Using the recently developed time-dependent second-order Moller-Plesset perturbation theory (TDMP2), we have calculated correlated frequency-dependent multipole polarizabilities for the noble gases argon through radon. To get accurate results, i.e., near the TDMP2 basis set limit, we considered large one-particle basis sets, optimized for polarizability calculations. With the exception of argon, where we assumed relativistic effects to be neglegible, we employed the spin-free Hamiltonian obtained by means of a Douglas-Kroll transformation to treat relativistic and correlation effects on equal footing. Where reference data are available, the results for the static values and for the first Cauchy moments of all polarizabilities considered are in good agreement with the best theoretical and experimental data. Utilizing these results, we have calculated improved dispersion coefficients for interactions involving the rare gas atoms Ar through Rn, which are estimated to be accurate within a few percent.