The kinetic-energy-dependent cross sections for the reactions of Co(n)+ (n = 2-16) with D2 are measured as a function of kinetic energy over a range of 0-8 eV in a guided ion-beam tandem mass spectrometer. The observed products are Co(n) D+ for all clusters and Co(n)D2+ for n = 4,5,9-16. Reactions for the formation of Co(n)D+ (n = 2-16) and Co9D2+ are observed to exhibit thresholds, whereas cross sections for the formation of Co(n)D2+ (n = 4,5,10-16) exhibit exothermic reaction behavior. The Co(n)+-D bond energies as a function of cluster size are derived from the threshold analysis of the kinetic-energy dependence of the endothermic reactions and are compared to previously determined metal-metal bond energies, D0(Co(n)+-Co). The bond energies of Co(n)+-D generally increase as the cluster size increases, and roughly parallel those for Co(n)+-Co for clusters n > or = 4. These trends are explained in terms of electronic and geometric structures for the Co(n)+ clusters. The bond energies of Co(n)+-D for larger clusters (n > or = 10) are found to be very close to the value for chemisorption of atomic hydrogen on bulk-phase cobalt. The rate constants for D2 chemisorption on the cationic clusters are compared with the results from previous work on cationic and neutral cobalt clusters.