A calculation of deuteron Compton scattering using non-relativistic perturbation theory is presented, with the primary motivation of investigating the feasibility of determining the neutron polarizabilities from this type of experiment. This calculation is expected to be valid for energies below 100 MeV. Pion-exchange, relativistic, and recoil corrections are also included. The lowenergy theorem for gauge invariance is shown to be satisfied. The relative effects of the different terms and their effects on the determinations of the polarizabilities are discussed at energies of 49, 69, and 95 MeV. The cross-section is dominated by the seagull, polarizability, and electromagnetic multipole interactions. Relativistic and pion-exchange terms are also important, while recoil corrections and multipoles of L=2 and greater are negligible. The calculation provides a reasonable description of the experimental data points at 49 and 69 MeV. The polarizabilities are difficult to determine at these energies. A more accurate determination of the polarizabilities may be possible at 95 MeV.