  The coherent reaction, $\gamma d \rightarrow \pi^0\pi^0 d$ was studied with
the BGOOD experiment at ELSA from threshold to a centre-of-mass energy of
2850\,MeV. A full kinematic reconstruction was made, with final state deuterons
identified in the forward spectrometer and $\pi^0$ decays in the central BGO
Rugby Ball. The strength of the differential cross section exceeds what can be
described by models of coherent photoproduction and instead supports the three
isoscalar dibaryon candidates reported by the ELPH collaboration at 2.38, 2.47
and 2.63\,GeV/c$^2$. A low mass enhancement in the $\pi^0\pi^0$ invariant mass
is also observed at the $d^*(2380)$ centre-of-mass energy which is consistent
with the ABC effect. At higher centre-of-mass energies, a narrow peak in the
$\pi^0 d$ invariant mass at 2114\,MeV/c$^2$ with a width of 20\,MeV/c$^2$
supports a sequential two-dibaryon decay mechanism.
