Electron-intramolecular-phonon coupling and its role in the occurrence of possible superconductivity in the monoanions of coronene (C24H12) and corannulene (C20H10) are studied. Electron-intramolecular-phonon coupling constants are calculated from the intramolecular vibronic coupling constants. The C-C stretching E-2g mode of 1668 cm(-1) plays an essential role in the electron-intramolecular-phonon coupling in the monoanion of coronene while the low frequency E-2 modes, which have a radial character, and the C-C stretching mode of 1669 cm(-1), which has a tangential character, afford large electron-intramolecular-phonon coupling constants in the monoanion of corannulene. The calculated total electron-intramolecular-phonon coupling constant for the monoanion of corannulene (0.269 eV) is much larger than that for coronene monoanion (0.076 eV). The intermediate characteristics between sigma and pi orbital interaction properties owing to the bowl-shaped structure of corannulene make orbital interactions between two neighboring carbon atoms strong, and thus electron-intramolecular-phonon coupling is stronger in the monoanion of corannulene than that in the monoanion of coronene. Possible superconducting transition temperature T-c value for the monoanion of corannulene is estimated to be an order of magnitude larger than that for the monoanion of coronene; for example, the calculated values of T(c)s for the monoanions of coronene and corannulene are about 0.05-8.86 and 29.17-65.56 K, respectively, in the range of n(0)=4-5 and mu*=0.10-0.20, where n(0) is the density of states at the Fermi level (states per eV, per spin, and per molecule) and mu* is the Coulomb pseudopotential. The relationships between structures and T(c)s in alkali-doped A(3)C(60) complexes and graphite intercalation compounds (GICs) are also discussed from a viewpoint that corannulene can be viewed as a fragment of C-60 and coronene as a fragment of one-sheet graphite.