The 4.67 micrometer absorption feature of solid CO is an important signature of grain mantles in molecular clouds. This paper presents new observations of solid CO absorption in the spectra of four infrared sources in and behind the Serpens dark cloud. We also present supplementary 2.0-2.5 micrometer spectra which clarify the nature of selected sources. Solid CO profiles are compared with models based on laboratory data. In common with previous studies of other clouds, we find that the observed profiles are consistent with the presence of two distinct phases of CO-bearing ice, one dominated either by CO itself or by CO mixed with absorption relative to that of the water-ice feature at 3.1 micrometers is unusually high in Serpens: we deduce column densities for CO and H2O in solid form and conclude that the mean CO abundance in dust is 40% of the H2O abundance, compared with values in the range 0%-30% typical of other molecular clouds. On the basis of its 2.0-2.5 micrometer spectrum and near-infrared colors, we deduce the infrared source CK 2 to be a K5-M0 III field star situated behind the Serpens cloud and suffering 40-50 mag of visual extinction. Assuming empirical correlations between extinction and total (gas + dust) CO column density, we estimate the CO depletion (i.e., the fraction of interstellar CO in the line of sight tied up in grains) to be approximately 40% in the intracloud medium of the Serpens cloud, comparable with previous estimates for the Taurus dark cloud, and much higher than that found in the environments of protostellar objects.