Magnetic monolayer and bilayer Co islands of only a few nanometer in size were grown by atomic deposition on atomically flat Au(111) films. The islands were studied in situ by scanning tunneling microscopy (STM) and spectroscopy at low temperatures. Spin-resolved tunneling spectroscopy, using an STM tip with a magnetic coating, revealed that the Co islands exhibit a net magnetization perpendicular to the substrate surface due to the presence of spin-polarized d-states. A random distribution of islands with either upward or downward pointing magnetization was observed, without any specific correlation of magnetization orientation with island size or island height.