Positron-electron annihilation spectra of benzene, deuterated benzene, and naphthalene were theoretically calculated as a function of positron collision energy using Feshbach vibrational resonance energies and widths, which can be obtained from the correlation-polarization-potential model. We found that the contribution of overtone excitations to the annihilation spectrum becomes large for the vibrational mode, where structural deformation along the corresponding vibrational coordinate significantly changes the positron binding energy and polarizability. This behavior occurs for the ${\ensuremath{\nu}}_{2}$ vibrational mode in benzene and deuterated benzene, corresponding to symmetric ring stretching. Since the incoming positron is dominantly attracted by the \ensuremath{\pi} electrons of benzene, we conclude that the ring stretching vibration largely affects the \ensuremath{\pi}-electron density of the benzene ring.