The criticality eigenvalue problems of both multigroup diffusion and transport theories have slow rates of convergence when the dominance ratio is close to one. This situation arises especially in the analysis of loosely coupled reactor systems and necessitates the use of acceleration techniques. The coarse mesh rebalance method constitutes one of the prominent ones of such acceleration schemes. The coarse mesh rebalance method has been used in the acceleration of direct diffusion criticality eigenvalue problems. In this study, this acceleration method is utilized also in the solution of adjoint diffusion problems in spherical geometry. The efficiency of the acceleration method is assessed through numerical experiments and certain conclusions have been drawn regarding the use of coarse mesh rebalance in such problems.