We have measured the photoconductivity excitation spectra of individual semiconducting carbon nanotubes incorporated as the channel of field-effect transistors. In addition to the pronounced resonance that correlates with the second van Hove transition (E(22)) in semiconducting carbon nanotubes, a weaker sideband at about 200 meV higher energy is observed. Electronic structure calculations that include electron-phonon coupling indicate that the spectra originate from the simultaneous excitation of an exciton (main resonance) and a C-C bond stretching phonon (sideband). The spectral features are not compatible with an interband interpretation of the excitation involved.