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Alloying is a successful strategy for tuning the phases and properties of two-dimensional (2D) transition metal dichalcogenides (TMDCs). To accelerate the synthesis of new TMDC alloys, we present a method for generating temperature-composition equilibrium phase diagrams by combining first-principles total energy calculations with thermodynamic solution models. This method is applied to three representative 2D TMDC alloys: an isostructural alloy, MoS2(1-x)Te2x, and two heterostructural alloys, Mo1-xWxTe2 and WS2(1-x)Te2x. We show that the mixing enthalpy of the entire composition range of these binary alloys can be reliably represented using a sub-regular solution model fitted to the total energy of a small number of compositions that are calculated using density-functional theory on special quasi-random structures. The sub-regular solution model uses a cubic fit that captures three-body effects that are important in these TMDC alloys having hexagonal structures. By comparing both isostructural and heterostructural phase diagrams generated with this method to those calculated with cluster expansion methods, we demonstrate that this method can be used to rapidly design phase diagrams of TMDC alloys, and related 2D materials.