The second-order nonlinear optical rectification coefficient (ORC) associated with intersubband transitions in a hydrogenic quantum ring (QR) with a two-dimensional pseudopotential in the presence of an external magnetic field is theoretically investigated. Calculations are performed by using the perturbation method and the compact density-matrix approach within the effective mass approximation. Based on the computed energies and wave functions, we have investigated the effects of the hydrogenic impurity, an external magnetic field, the geometrical size and the chemical potential of the pseudopential on this coefficient. Our results show that the second-order nonlinear ORCs of a hydrogenic QR are strongly affected by the geometrical size and chemical potential of the pseudopential, the hydrogenic impurity and the external magnetic field.