Coherent double neutral-pion photoproduction on the deuteron, $gamma{d}${$to$}$pi^0pi^0{d}$, has been experimentally studied at incident photon energies ranging from 0.75 to 1.15 GeV. The total cross section as a function of the $gamma{d}$ center-of-mass energy shows resonance-like behavior, which peaks at approximately 2.47 and 2.63 GeV. The measured angular distribution of deuteron emission is rather flat, which cannot be reproduced by the kinematics of quasi-free $pi^0pi^0$ production with deuteron coalescence. In $pi^0d $ invariant-mass distributions, a clear peak is observed at $2.14{pm}0.01$ GeV$/c^2$ with a width of $0.09{pm}0.01$ GeV$/c^2$. The spin-parity of this state is restricted to $1^+$, $2^+$ or $3^-$ from the angular distributions of the two $pi^0$s. The present work shows strong evidence for the existence of an isovector dibaryon resonance with a mass of 2.14 GeV$/c^2$. The $2^+$ assignment is consistent with the theoretically predicted ${cal{D}}_{12}$ state, and also with the energy dependence of the $pi{d}$ partial-wave amplitude $^3!P_2$ for the $pi^{pm}d${$to$}$pi^{pm}d$ and $pi^+d${$to$}${pp}$ reactions.
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