Azimuthal asymmetries in exclusive electroproduction of a real photon from an unpolarized deuterium target are measured with respect to beam helicity and charge. They appear in the distribution of these photons in the azimuthal angle phi around the virtual-photon direction, relative to the lepton scattering plane. The extracted asymmetries are attributed to either the deeply virtual Compton scattering process or its interference with the Bethe-Heitler process. They are compared with earlier results on the proton target. In the measured kinematic region, the beam-charge asymmetry amplitudes and the leading amplitudes of the beam-helicity asymmetries on an unpolarized deuteron target are compatible with the results from unpolarized protons.