Superconductivity in the new polymerized C60 fullerite clathrate doped with simple metals was investigated through density functional theory methods. The phonon dispersion curves were systematically computed for the clathrate structures containing the guest dopants (Li, Na, K, Be, Mg, Ca, Al, Ga, Ge) in one of the two distinct cages, fullerene-like C60 and sodalite-like C24, exhibited by this structure. Only four of these structures, Li@C24, Na@C24, Ga@C24 and Be@C60, are dynamically stable in the harmonic approximation. They all show superconducting behavior, although their critical temperatures are predicted to be below 2 K.