Size and stoichiometry-dependent magnetic properties of deposited Co and CoPt alloy clusters on a Ni/Cu(100) substrate have been investigated by use of x-ray magnetic circular dichroism spectroscopy. Using sum rules, spin and orbital moments were extracted from the spectra. Spin and orbital moments show a strong size-dependent effect with a tendency for an increase with cluster size, which is in contrast to observations for Co clusters on a Pt(111) surface. Addition of a Pt atom to a Co dimer leads to a doubling of the orbital moment. CoPt clusters show a strong increase in chemical reactivity towards oxidation. The resulting ConPtOx clusters show a ratio of orbital to spin moment comparable to the pure clusters, however, with a strong suppression of the absolute orbital and spin moments.