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.