  We present ALMA CO (2-1) detections in 11 gas-rich cluster galaxies at z~1.6,
constituting the largest sample of molecular gas measurements in z>1.5 clusters
to date. The observations span three galaxy clusters, derived from the Spitzer
Adaptation of the Red-sequence Cluster Survey. We augment the >5sigma
detections of the CO (2-1) fluxes with multi-band photometry, yielding stellar
masses and infrared-derived star formation rates, to place some of the first
constraints on molecular gas properties in z~1.6 cluster environments. We
measure sizable gas reservoirs of 0.5-2x10^11 solar masses in these objects,
with high gas fractions and long depletion timescales, averaging 62% and 1.4
Gyr, respectively. We compare our cluster galaxies to the scaling relations of
the coeval field, in the context of how gas fractions and depletion timescales
vary with respect to the star-forming main sequence. We find that our cluster
galaxies lie systematically off the field scaling relations at z=1.6 toward
enhanced gas fractions, at a level of ~4sigma, but have consistent depletion
timescales. Exploiting CO detections in lower-redshift clusters from the
literature, we investigate the evolution of the gas fraction in cluster
galaxies, finding it to mimic the strong rise with redshift in the field. We
emphasize the utility of detecting abundant gas-rich galaxies in high-redshift
clusters, deeming them as crucial laboratories for future statistical studies.
