We determined the zero-temperature phase diagram of D₂ physisorbed on graphane using the diffusion Monte Carlo method. The substrate used was C-graphane, an allotropic form of the compound that has been experimentally obtained through hydrogenation of graphene. We found that the ground state is the δ phase, a commensurate structure observed experimentally when D₂ is adsorbed on graphite, and not the registered √3 x √3 structure characteristic of H₂ on the same substrate.