Magnetic anisotropy slows down magnetic relaxation and plays a prominent role in the design of permanent magnets. Coordination compounds of Co(II) in particular exhibit large magnetic anisotropy in the presence of low-coordination environments and have been used as single-molecule magnet prototypes. However, only a limited sampling of cobalt's vast chemical space has been performed, potentially obscuring alternative chemical routes toward large magnetic anisotropy. Here we perform a computational high-throughput exploration of Co(II)'s chemical space in search of new single-molecule magnets. We automatically assemble a diverse set of ∼15,000 novel complexes of Co(II) and fully characterize them with multireference ab initio methods. More than 100 compounds exhibit magnetic anisotropy comparable to or larger than leading known compounds. The analysis of these results shows that compounds with record-breaking magnetic anisotropy can also be achieved with coordination four or higher, going beyond the established paradigm of two-coordinated linear complexes.