Doping of metal oxides can be used to modify their reactivity with respect to oxygen vacancy formation and molecular adsorption, key reactions in the applications of oxides in catalysis. In this article, we study the effects of Ti, Zr, and Hf doping on CO adsorption on the (110) surface of cerium dioxide and NO adsorption at the same surface with oxygen vacancy defects, using density functional theory, corrected for on-site Coulomb interactions (DFT+U). The dopants substitute a Ce atom in the surface layer, resulting in strong structural distortions to the surface and smaller oxygen vacancy formation energies compared to the undoped surface. On the doped surfaces, CO adsorbs much more strongly compared to the undoped surface, forming a structure similar to a carbonate unit [(CO(3))(2-)], in which a CO(2) unit points away from the surface. The presence of a carbonate is confirmed by analysis of the electronic structure and vibrational frequencies. On the defective surface with one oxygen vacancy, NO adsorption is weak, so that NO sits above a defective surface. Consistent with the literature, adsorption of two NO molecules at neighboring vacancy sites results in strong adsorption and formation of a N-N-like bond, as well as lengthening of the N-O bonds. However, the energetics of this process at the doped surfaces are not as favorable as at the undoped surface. Computed energetics for CO oxidation and NO reduction show that improving the oxidative power of the oxide makes molecular reduction less favorable.