We apply to transition metal monoxides the self-interaction corrected (SIC) local spin density approximation, implemented locally in the multiple scattering theory within the Korringa-Kohn-Rostoker (KKR) band structure method. The calculated electronic structure and in particular magnetic moments and energy gaps are discussed in reference to the earlier SIC results obtained within the linear muffin-tin orbital atomic sphere approximation band structure method, involving transformations between Bloch and Wannier representations, in order to solve the eigenvalue problem and calculate the SIC charge and potential. Since the KKR method can be easily extended to treat disordered alloys, by invoking the coherent potential approximation (CPA), in this paper we compare the CPA approach and supercell calculations to study the electronic structure of NiO with cation vacancies.