A study of the layered triangular lattice materials ${\mathrm{K}}_{2}\mathrm{Co}{({\mathrm{SeO}}_{3})}_{2}$ and ${\mathrm{Rb}}_{2}\mathrm{Co}{({\mathrm{SeO}}_{3})}_{2}$ is reported. These isostructural compounds crystallize in the trigonal space group $R\ensuremath{-}3m$ (No. 166). The magnetic $\mathrm{C}{\mathrm{o}}^{2+}$ ions form a spin-1/2 triangular lattice and display strongly frustrated magnetism. We find no evidence in the susceptibility or heat capacity for in-plane ordering of the spins; rather the in-plane inverse susceptibility is typical of that seen for frustrated magnets. At around 10 K, a ferromagnetic component appears in the magnetic susceptibility perpendicular to the triangular planes. The heat capacity at low applied fields does not show sharp features, but in larger applied fields a sharp ferromagneticlike transition appears. Field- and direction-dependent magnetization measurements at 2 K indicate that both materials have a magnetic easy axis perpendicular to the triangular planes. The magnetic properties are sensitive to the field applied perpendicular to the triangular planes, which induces a metamagnetization transition at 0.75 T. Spin polarization develops along with the increasing out-of-plane field, resulting in a saturated ferromagnetic state at high fields. In contrast, the magnetic properties are resistant to the in-plane field. Our results suggest that these materials are embodiments of Ising spins on triangular lattices with easy-axis anisotropy.