Determining the nature and modes of star formation at galactic scales requires an understanding of the relationship between the gas content of a galaxy and its star formation rate. Remarkable progress has been made in understanding the conversion mechanisms in field galaxies, but the cold and dense gas fueling the star formation in galaxies inside clusters has been investigated much less often. We present the first CO observations of luminous infrared galaxies (LIRGs) inside the virial radii of two intermediate redshift clusters, CL1416+4446 (z = 0.397) and CL0926+1242 (z = 0.489). We detect three galaxies at high significance (5 to 10 sigma), and provide robust estimates of their CO luminosities L'(CO). To put our results into a general context, we revisit the relation between cold and hot gas and stellar mass in nearby field and cluster galaxies. We find evidence that at fixed L-IR (or fixed stellar mass), the frequency of high L'(CO) galaxies is lower in clusters than in the field, suggesting environmental depletion of the reservoir of cold gas. The level of star formation activity in a galaxy is primarily linked to the amount of cold gas, rather than to the galaxy mass or the lookback time. In clusters, just as in the field, the conversion between gas and stars seems universal. The relation between L-IR and L'(CO) for distant cluster galaxies extends the relation of nearby galaxies to higher IR luminosities. Nevertheless, the intermediate redshift galaxies fall well within the dispersion of the trend defined by local systems. Considering that L'(CO) is generally derived from the CO(1-0) line and sensitive to the vast majority of the molecular gas in the cold interstellar medium of galaxies, but less to the part which will actually be used to form stars, we suggest that molecular gas can be stripped before the star formation rate is affected. Combining our sample with others, we find evidence for a decrease in CO towards the cluster centers. This is the first hint of an environmental impact on cold gas at intermediate redshift.