  The coherent reaction, $\gamma d \rightarrow \pi^0\eta d$ was studied with
the BGOOD experiment at ELSA from threshold to a centre-of-mass energy of
3200\,MeV. A full kinematic reconstruction was made, with final state deuterons
identified in the forward spectrometer and $\pi^0$ and $\eta$ decays in the
central BGO Rugby Ball. The strength of the differential cross section exceeds
what can be described by models of coherent photoproduction at forward angles
by orders of magnitude. The distribution of the differential cross section has
an excellent agreement with a model including quasi-free $\Delta \pi$
photoproduction, pion re-scattering and $N(1535)$ formation and subsequent
nucleon coalescence to the deuteron. This also gives a reasonable description
of the two-body invariant mass distributions and naturally explains the similar
magnitudes of this channel and $\pi^0\pi^0 d$ coherent photoproduction.
