© 2018 American Physical Society. Significant excesses of J/ψ yield at very low transverse momentum (pT<0.3 GeV/c) were observed by the ALICE and STAR collaborations in peripheral hadronic A+A collisions. This is a sign of coherent photoproduction of J/ψ in violent hadronic interactions. Theoretically, the photoproduction of J/ψ in hadronic collisions raises questions about how spectator and nonspectator nucleons participate in the coherent reaction. We argue that the strong interactions in the overlapping region of incoming nuclei may disturb the coherent production, leaving room for different coupling assumptions. The destructive interference between photoproduction on ions moving in opposite directions also needs to be included. This paper presents calculations of J/ψ production from coherent photon-nucleus (γ+A→J/ψ+A) interactions in hadronic A+A collisions at BNL Relativistic Heavy Ion Collider and CERN Large Hadron Collider energies with both nucleus and spectator coupling hypotheses. The integrated yield of coherent J/ψ as a function of centrality is found to be significantly different, especially towards central collisions, for different coupling scenarios. Differential distributions as a function of transverse momentum, azimuthal angle, and rapidity in different centrality bins are also shown, and found to be more sensitive to the Pomeron coupling than to the photon coupling. These predictions call for future experimental measurements to help better understand the coherent interaction in hadronic heavy-ion collisions.