We analyze the magnetic properties of three mononuclear Co(II) coordination complexes using quantum chemical complete active space self-consistent field and N-electron valence perturbation theory approaches. The complexes are characterized by a distorted tetrahedral geometry in which the central ion is doubly chelated by the icosahedral ligands derived from 1,2-(HS)2-1,2-C2B10H10 (complex I), from 1,2-(HS)2-1,2-C2B10H10 and 9,12-(HS)2-1,2-C2B10H10 (complex II), and from 9,12-(HS)2-1,2-C2B10H10 (complex III), which are two positional isomers of dithiolated 1,2-dicarba-closo-dodecaborane (complex I). Complex I was realized experimentally recently (Tu, D.; Shao, D.; Yan, H.; Lu, C. Chem. Commun. 2016, 52, 14326) and served to validate the computational protocol employed in this work, while the remaining two proposed complexes can be considered positional isomers of I. Our calculations show that these complexes present different axial and rhombic zero-field splitting anisotropy parameters and different values of the most significant components of the g tensor. The predicted axial anisotropy D = -147.2 cm-1 for complex II is twice that observed experimentally for complex I, D = 72.8 cm-1, suggesting that this complex may be of interest for practical applications. We also analyze the temperature dependence of the magnetic susceptibility and molar magnetization for these complexes when subject to an external magnetic field. Overall, our results suggest that o-carborane-incorporated Co(II) complexes are worthwhile candidates for experimental exploration as single-ion molecular magnets.