Non-planar (cylindrical and spherical) double layers (DLs) in two-ion-temperature dusty plasma, whose constituents are inertial negative dust, ions with two distinctive temperatures, and Boltzmann electrons, are studied by employing the reductive perturbation method. The modified Gardner equation describing the nonlinear propagation of dust-acoustic (DA) waves is derived, and its non-planar double layer solutions are analyzed numerically. The parametric regimes for the existence of DA DLs, which are found to be associated with positive potential only, are obtained. The basic features of non-planar DA DLs, which are found to be different from planar ones, are also identified. The implications of our results to different space and laboratory dusty plasma situations are discussed.