We calculate the coherent charmonium photoproduction in the photon energy domain where the coherence and formation lengths exceed the average internucleon distance in nuclei but are comparable to the nuclear radii. In this kinematical regime we use the generalized vector dominance model (GVDM) adjusted to account for the physics of bound charmonium states and for the color screening phenomenon. We find significant oscillations in the energy dependence of the total and forward photoproduction cross sections due to the oscillating behavior of the longitudinal nuclear form factor. Within the GVDM these oscillations are strongly modified by the nondiagonal rescatterings of the charmonium. We demonstrate how to employ the oscillating behavior of the photoproduction cross sections off nuclear targets to determine the elementary charmonium photoproduction amplitudes and the genuine charmonium-nucleon cross sections in the forthcoming SLAC E160 experiment.