  Coherent eta photoproduction on the deuteron is studied in the $S_{11}$
resonance region neglecting eta rescattering and two-body processes. For the
elementary reaction on the nucleon, we have considered the dominant
$S_{11}(1535)$ resonance and as background the nucleon pole terms as well as
$\rho$ and $\omega$ meson exchange. We have studied the influence of different
choices for the neutron resonance amplitude, different prescriptions for fixing
the invariant mass of the resonance amplitude and different methods for
deriving the elementary production amplitude for an arbitrary reference frame.
