The exclusive photoproduction of the heavy vector mesons $\psi$'s and $Y$'s is investigated in peripheral lead-lead collisions for the energies available at the LHC, $\sqrt{s}=2.76$ TeV and $\sqrt{s}=5.02$ TeV. In order to evaluate the robustness of the light-cone color dipole formalism, previously tested in the ultraperipheral regime. It was calculated the rapidity distribution as well as the nuclear modification factor ($R_{AA}$) for the three centrality classes: 30%-50%, 50%-70% and 70%-90%. The transition from ultraperipheral to peripheral regime was carried out sophisticating the photon flux description and the photonuclear cross section, taking into account the effective interaction area. In our calculations, three scenarios were considered: (scenario 1) the direct application of the usual photon flux and of the photonuclear cross section without any relevant change in relation to the UPC's, (scenario 2) the application of an effective photon flux keeping the photonuclear cross section unchanged and (scenario 3) where it was also considered an effective photonuclear cross section. The results obtained from the three scenarios were compared with the ALICE measurements (only $J/\psi$ at the moment), showing a better agreement with the data in the more complete approach (scenario 3), mainly in the more central regions (30%-50% and 50%-70%) where the incertainty is smaller.