We address the intramolecular vibronic interactions in the C-36 tri- and tetra-anions to understand the Jahn-Teller effects and possible superconductivity in "electron-doped" C-36 solids. We use the B3LYP hybrid Hartree-Fock/density-functional-theory method for our theoretical analyses. Neither the highest occupied molecular orbital (HOMO) nor the lowest unoccupied molecular orbital (LUMO) of the C-36 molecule with D-6h symmetry are degenerate, but the next LUMO is twofold degenerate. One can therefore expect Jahn-Teller distortions and interesting electronic properties in the C-36 anions. Computed vibronic and electron-phonon coupling constants of the tetra-anion are about twice as large as those of the tri-anion. The second lowest Jahn-Teller active E-2g mode of 561 cm(-1) is predicted to have the largest coupling constants in both anions. We calculate superconducting transition temperature T-c from McMillan's formula using the coupling constants as well as electronic densities of states at the Fermi level and Coulomb pseudopotentials as parameters.