We perform an electronic structure study for cerium oxide homogeneously doped with cobalt impurities, focusing on the role played by oxygen vacancies and structural relaxation. By means of full-potential ab initio methods, we explore the possibility of ferromagnetism as observed in recent experiments. Our results indicate that oxygen vacancies seem to be crucial for the appearance of a ferromagnetic alignment among Co impurities, obtaining an increasing tendency towards ferromagnetism with growing vacancy concentration. However, the estimated couplings cannot explain the experimentally observed room-temperature ferromagnetism. In this systematic study, we draw relevant conclusions regarding the location of the oxygen vacancies and the magnetic couplings involved. In particular, we find that oxygen vacancies tend to nucleate in the neighborhood of Co impurities and we get a remarkably strong ferromagnetic coupling between Co atoms and the Ce³⁺ neighboring ions. The calculated magnetic moments per cell depend on the degree of reduction, which could explain the wide spread in the magnetization values observed in the experiments.