We investigate coherent π0-photoproduction on the deuteron near threshold with special emphasis on beam-target double spin asymmetries. We present results for the spin asymmetries $T^{c}_{1M}$ (M = 0, 1) for circular polarized photons and vector polarized deuterons, $T^{c}_{2M}$ (M = 1, 2) for circular polarized photons and tensor polarized deuterons, $T^{l}_{1M}$ (M = 0, ± 1) for longitudinal polarized photons and vector polarized deuterons, and $T^{l}_{2M}$ (M = 0, ± 1, ± 2) for longitudinal polarized photons and tensor polarized deuterons in the γd → π0d reaction near threshold. We also discuss the sensitivity of the estimated results to the D-wave component of the deuteron wave function. The unitary isobar MAID-2007 model is used for the elementary γN → πN amplitude. This model is parameterized in terms of invariant amplitudes and allows one to give a more reliable description of the threshold region. The realistic and high-precision Bonn NN potential (full model) is used for the deuteron wave function. We have found that the D-wave component of the deuteron wave function has a little effect on the $T^{c}_{1M}$ (M = 0, 1) and $T^{l}_{2M}$ (M = 0, 1, 2) spin asymmetries. On the contrary, we have obtained a significant role of the D-wave component on the spin asymmetries $T^{c}_{2M}$ (M = 1, 2), $T^{l}_{1M}$ (M = 0, ± 1), and $T^{l}_{2M}$ (M = − 1,− 2).