  We report the serendipitous discovery of an overdensity of CO emitters in an
X-ray-identified cluster (Log$_{10}$M$_{\rm halo}/M_{\odot}\sim13.6$ at
z=1.3188) using ALMA. We present spectroscopic confirmation of 6 new cluster
members exhibiting CO(2-1) emission, adding to 2 existing optical/IR
spectroscopic members undetected in CO. This is the lowest mass cluster to date
at z>1 with molecular gas measurements, bridging the observational gap between
galaxies in the more extreme, well-studied clusters (Log$_{10}$~M$_{\rm
halo}/M_{\odot}\gtrsim14$) and those in group or field environments at cosmic
noon. The CO sources are concentrated on the sky (within ~1-arcmin diameter)
and phase space analysis indicates the gas resides in galaxies already within
the cluster environment. We find that CO sources sit in similar phase space as
CO-rich galaxies in more massive clusters at similar redshifts (have similar
accretion histories) while maintaining field-like molecular gas reservoirs,
compared to scaling relations. This work presents the deepest CO survey to date
in a galaxy cluster at z>1, uncovering gas reservoirs down to M$_{\rm
H_{2}}>1.6\times10^{10}$M$_{\odot}$ (5$\sigma$ at 50% primary beam). Our deep
limits rule out the presence of gas content in excess of the field scaling
relations; however, combined with literature CO detections, cluster gas
fractions in general appear systematically high, on the upper envelope or above
the field. This study is the first demonstration that low mass clusters at
z~1-2 can host overdensities of CO emitters with surviving gas reservoirs, in
line with the prediction that quenching is delayed after first infall while
galaxies consume the gas bound to the disk.
