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The total cross sections were measured for coherent double neutral-pionphotoproduction on the deuteron at incident energies below 0.9 GeV for thefirst time. No clear resonance-like behavior is observed in the excitationfunction for $W_{\gamma d}=2.38$--2.61 GeV, where the $d^*(2380)$ dibaryonresonance observed at COSY is expected to appear. The measured excitationfunction is consistent with the existing theoretical calculation for thisreaction. The upper limit of the total cross section is found to be$0.034$~$\mu$b for the dibaryon resonance at $W_{\gamma d}=2.37$~GeV (90\%confidence level) in the $\gamma d \to \pi^0\pi^0 d$ reaction.

First measurement of coherent double neutral-pion photoproduction on the deuteron at incident energies below 0.9 GeV