Coincidence γ-ray spectrometers are promising candidates for future radionuclide monitoring systems, due to their improved minimum detectable activity (MDA) compared to most single-detector systems. To evaluate the performance of future detector designs, a simulation approach to determining MDA using the Geant4 toolkit is proposed in this work. In particular, a phenomenological γ-ray background model was developed and validated against γ-ray coincidence measurements in unshielded and shielded environments. The background model performs well in the unshielded case, where single γ-ray background dominates, but underestimates coincidence spectra in the shielded case. An example of how MDA can be calculated as a function of a detector design parameter is presented to facilitate future detector optimization work.