Spin-averaged and spin-polarized scanning tunneling spectroscopy at low temperature was performed on nanometer-scale triangular Co islands grown epitaxially on Cu(111) in the submonolayer coverage regime. Two structurally different island types can clearly be distinguished by their spin-averaged electronic structure. Spin-polarized measurements allow a separation of spectral contributions arising from different island stacking or from opposite magnetization states, respectively. In an applied magnetic field, both island types are found to be magnetized perpendicular to the surface, with large values of saturation field, remanence, and coercivity.