Coherent π-photoproduction off the deuteron near η-threshold is investigated within an approach which includes the amplitudes of impulse approximation, two-step process with πN- and ηN-rescattering, and intermediate ηNN interaction. Results for unpolarized and polarized cross sections as well as for all possible polarization observables with polarized photons and/or oriented deuterons are predicted and compared with available data, and differences with other theoretical models are analyzed. The contribution of this reaction to the deuteron spin asymmetry is calculated and its contribution to the GDH integral is explicitly evaluated by integration up to a photon energy of 900 MeV. In addition, the sensitivity of the results to the elementary amplitude and the choice of the NN potential model governs the deuteron wave function is also investigated. This work is motivated by the measurements of the CLAS Collaboration at Jefferson laboratory, where a cusp-like structure in the energy dependence of the differential cross section has been observed at extremely backward pion angles.