Binary alloys present a promising venue for band gap engineering and tuning of other mechanical and electronic properties of materials. Here we use the density-functional theory and cluster expansion to investigate the thermodynamic stability and electronic properties of 2D transition metal dichalcogenide (TMD) binary alloys. We find that mixing electron-accepting or electron-donating transition metals with 2D TMD semiconductors leads to degenerate p- or n-doping, respectively, effectively rendering them metallic. We then proceed to investigate the electronic properties of semiconductor-semiconductor alloys. The exploration of the configurational space of the 2D molybdenum-tungsten disulfide (Mo1-xWxS2) alloy beyond the mean field approximation yields insights into anisotropy of the electron and hole effective masses in this material. The effective hole mass in the 2D Mo1-xWxS2 is nearly isotropic and is predicted to change almost linearly with the tungsten concentration x. In contrast, the effective electron mass shows significant spatial anisotropy. The values of the band gap in 2D Mo1-xWxS2 and MoSe2(1-x)S2x are found to be configuration-dependent, exposing the limitations of the mean field approach to band gap analysis in alloys.