In this work we present a computational analysis of a new family of magnetic Co(II) single-ion complexes with large magnetic anisotropy based on icosahedral and octahedral carborane ligands. In particular, we extend our previous computational work on mononuclear Co(II) complexes with 1,2-(HS)(2)-1,2-C2B10H10 and 9,12-(HS)(2)-1,2-C2B10H10 icosahedral o-carborane ligands to a larger set of complexes where the Co(II) ion is doubly chelated by those ligands and by other two positional isomers belonging to the 1,2-dicarba-closo-dodeca-borane family. We also describe Co(II) complexes with octahedral ligands derived from 1,2-dicarba-closo-hexaborane and study the effects of replacing a thiol group by a hydroxy group in both polyhedral geometries, as well as the influence of the position of the carbon atoms. On analysis of the results for a total of 20 complexes, our results show that carborane-based Co(II) single-ion compounds present a distorted-tetrahedral geometry, high-spin ground states, and high values for the magnetic anisotropy parameters. We point out which of these would be suitable candidates to be synthesized and used as molecular magnets.