Three mononuclear cobalt(II) tetranitrate complexes (A)[Co(NO)] with different countercations, PhP (1), MePhP (2), and PhAs (3), have been synthesized and studied by X-ray single-crystal diffraction, magnetic measurements, inelastic neutron scattering (INS), high-frequency and high-field EPR (HF-EPR) spectroscopy, and theoretical calculations. The X-ray diffraction studies reveal that the structure of the tetranitrate cobalt anion varies with the countercation. 1 and 2 exhibit highly irregular seven-coordinate geometries, while the central Co(II) ion of 3 is in a distorted-dodecahedral configuration. The sole magnetic transition observed in the INS spectroscopy of 1-3 corresponds to the zero-field splitting (2(D + 3E)) from 22.5(2) cm in 1 to 26.6(3) cm in 2 and 11.1(5) cm in 3. The positive sign of the D value, and hence the easy-plane magnetic anisotropy, was demonstrated for 1 by INS studies under magnetic fields and HF-EPR spectroscopy. The combined analyses of INS and HF-EPR data yield the D values as +10.90(3), +12.74(3), and +4.50(3) cm for 1-3, respectively. Frequency- and temperature-dependent alternating-current magnetic susceptibility measurements reveal the slow magnetization relaxation in 1 and 2 at an applied dc field of 600 Oe, which is a characteristic of field-induced single-molecule magnets (SMMs). The electronic structures and the origin of magnetic anisotropy of 1-3 were revealed by calculations at the CASPT2/NEVPT2 level.