  We calculate the centrality dependence for coherent photoproduction of very
low-$p_{T}$ $J/\psi$ at Relativistic Heavy Ion Collider (RHIC) and Large Hadron
Collider (LHC) energies within the impact parameter dependent saturated color
dipole model. By using the large equivalent photon fluxes, we present the
differential cross section of very low-$p_{T}$ $J/\psi$ produced by coherent
photonuclear in peripheral heavy-ion collisions. The numerical results
demonstrate that our calculation are agree with $J/\psi$ data in peripheral
heavy ion collisions at Relativistic Heavy Ion Collider (RHIC) energies.
