Cross sections for elastic Compton scattering from the deuteron were measured over the laboratory angles straight theta(gamma) = 35 degrees -150 degrees. Tagged photons in the laboratory energy range E(gamma) = 84-105 MeV were scattered from liquid deuterium and detected in the large-volume Boston University NaI spectrometer. Using the calculations of Levchuk and L'vov, along with the measured differential cross sections, the isospin-averaged nucleon polarizabilities in the deuteron were estimated. A best-fit value of (alpha;-beta;) = 2.6+/-1.8 was determined, constrained by dispersion sum rules. This is markedly different from the accepted value for the proton of (alpha;-beta;)(p) = 10.0+/-1.5+/-0.9.