We studied the structure of the copper-cobalt (CuCo) surface alloy, formed by Co deposition on Cu(110), in dynamic equilibrium with CO. Using scanning tunneling microscopy (STM), we found that, in vacuum at room temperature and at low Co coverage, clusters of a few Co atoms substituting Cu atoms form at the surface. At CO pressures in the Torr range, we found that up to 2.5 CO molecules can bind on a single Co atom, in carbonyl-like configurations. Based on high-resolution STM images, together with density functional theory calculations, we determined the most stable CuCo cluster structures formed with bound CO. Such carbonyl-like formation manifests in shifts in the binding energy of the Co core-level peaks in X-ray photoelectron spectra, as well as shifts in the vibrational modes of adsorbed CO in infrared reflection absorption spectra. The multiple CO adsorption on a Co site weakens the Co-CO bond and thus reduces the C-O bond scission probability. Our results may explain the different product distribution, including higher selectivity toward alcohol formation, when bimetallic CuCo catalysts are used compared to pure Co.