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Identifying effective p-type transparent conducting oxides (TCOs) is an important factor in increasing the efficiency of technologies like flat panel displays and photovoltaic cells and requires overcoming the intrinsically high hole effective masses in pure TCOs caused by highly localized valence states with predominantly O-2p character. A first principles study, within density functional theory, using projector-augmented plane-waves (PAW) as implemented in the VASP code is presented on the effects of Mg-doping (replacing Al) on the conductivity and optical properties of 2H- CuAlO₂, AgAlO₂, and CuCrO₂. Exchange and correlation potentials are treated using the generalized gradient approximation (GGA) with a Hubbard correction, U, for the 3d(4d) orbitals of Cu/Cr(Ag), and the hybrid functional HSE06 for the bulk. GGA is used to obtain optical properties. The bulk is modelled using an 8-atom hexagonal primitive cell and a 64-atom hexagonal supercell, which is also used for the Mg-doped system. Obtained electronic and optical properties and calculated hole effective masses are presented in the context of results from literature and the effectiveness of Mg-doping on these TCOs is discussed.