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 φ 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.