The kinetic-energy dependence for the reactions of Co(n)+ (n=2-20) with O2 is measured as a function of kinetic energy over a range of 0 to 10 eV in a guided ion-beam tandem mass spectrometer. A variety of Co(m)+, Co(m)O+, and Co(m)O2+ (m < or = n) product ions is observed, with the dioxide cluster ions dominating the products for all larger clusters. Reaction efficiencies of Co(n)+ cations with O2 are near unity for all but the dimer. Bond dissociation energies for both cobalt cluster oxides and dioxides are derived from threshold analysis of the energy dependence of the endothermic reactions using several different methods. These values show little dependence on cluster size for clusters larger than three atoms. The trends in this thermochemistry and the stabilities of oxygenated cobalt clusters are discussed. The bond energies of Co(n)+-O for larger clusters are found to be very close to the value for desorption of atomic oxygen from bulk-phase cobalt. Rate constants for O2 chemisorption on the cationic clusters are compared with results from previous work on cationic, anionic, and neutral cobalt clusters.