  We report on an attempt to describe hard exclusive photoproduction of
$J/\Psi$ mesons, i.e. the reaction $\gamma p \to J/\Psi p$, by means of a
modified version of the hard-scattering approach, in which the proton is
treated as a quark-diquark rather than a three-quark system. In order to
improve the applicability of the model at momentum transfers of only a few GeV
we take into account constituent-mass effects in the calculation of the
perturbative scattering amplitude. With a standard $J/\Psi$-meson distribution
amplitude and diquark-model parameters adopted from preceding investigations of
other photon-induced reactions our predictions for differential cross sections
overestimate the naive extrapolation of the low-momentum transfer ZEUS data.
Our results, however, reveal the importance of taking into account the
charm-quark mass.
