  Deuteron Compton scattering is calculated to $\mathcal{O}(Q^2)$ in pionless
effective field theory using a dibaryon approach. The vector amplitude, which
was not included in the previous pionless calculations, contributes to the
cross section at $\mathcal{O}(Q^2)$ and influences significantly the extracted
values of nucleon electric polarizability at incident photon energy 49 MeV. We
recommend future high precision deuteron compton scattering experiments being
performed at 25-35 MeV photon energy where the nucleon polarizability effects
are appreciable and the pionless effective field theory is most reliable. For
example, a measurement at 30 MeV with a 3% error will constrain the isoscalar
nucleon electric polarizability $% \alpha_{0}$ with a $\sim 30%$ error.
