Ternary sulfides and selenides in the distorted-perovskite structure (“chalcogenide perovskites”) are predicted by theory to be semiconductors with band gap in the visible-to-infrared and may be useful for optical, electronic, and energy conversion technologies. Density functional theory can be used in combination with computational thermodynamics to predict the pressure-temperature phase diagrams for chalcogenide perovskites. We report results using the Strongly Constrained and Appropriately Normed (SCAN) and the rVV10 density functionals, and compare to previously-published results using the PBEsol functional. We highlight the windows of thermodynamic equilibrium between solid chalcogenide perovskites and the vapor phase at high temperature and very low pressure. These phase diagrams can guide adsorption-limited growth of ternary chalcogenides by molecular beam epitaxy (MBE).