The coherent photoproduction of J / ψ and ψ ′ mesons was measured in ultra-peripheral Pb–Pb collisions at a center-of-mass energy sNN=5.02 TeV with the ALICE detector. Charmonia are detected in the central rapidity region for events where the hadronic interactions are strongly suppressed. The J / ψ is reconstructed using the dilepton (l+l-) and proton–antiproton decay channels, while for the ψ ′ the dilepton and the l+l-π+π- decay channels are studied. The analysis is based on an event sample corresponding to an integrated luminosity of about 233 μb - 1. The results are compared with theoretical models for coherent J / ψ and ψ ′ photoproduction. The coherent cross section is found to be in a good agreement with models incorporating moderate nuclear gluon shadowing of about 0.64 at a Bjorken-x of around 6 × 10 - 4, such as the EPS09 parametrization, however none of the models is able to fully describe the rapidity dependence of the coherent J / ψ cross section including ALICE measurements at forward rapidity. The ratio of ψ ′ to J / ψ coherent photoproduction cross sections was also measured and found to be consistent with the one for photoproduction off protons.