  An understanding of the mass build-up in galaxies over time necessitates
tracing the evolution of cold gas (molecular and atomic) in galaxies. To that
end, we have conducted a pilot study called CO Observations with the LMT of the
Blind Ultra-Deep H I Environment Survey (COOL BUDHIES). We have observed 23
galaxies in and around the two clusters Abell 2192 (z = 0.188) and Abell 963 (z
= 0.206), where 12 are cluster members and 11 are slightly in the foreground or
background, using about 28 total hours on the Redshift Search Receiver (RSR) on
the Large Millimeter Telescope (LMT) to measure the $^{12}$CO J = 1 --> 0
emission line and obtain molecular gas masses. These new observations provide a
unique opportunity to probe both the molecular and atomic components of
galaxies as a function of environment beyond the local Universe. For our sample
of 23 galaxies, nine have reliable detections (S/N$\geq$3.6) of the $^{12}$CO
line, and another six have marginal detections (2.0 < S/N < 3.6). For the
remaining eight targets we can place upper limits on molecular gas masses
roughly between $10^9$ and $10^{10} M_\odot$. Comparing our results to other
studies of molecular gas, we find that our sample is significantly more
abundant in molecular gas overall, when compared to the stellar and the atomic
gas component, and our median molecular gas fraction lies about $1\sigma$ above
the upper limits of proposed redshift evolution in earlier studies. We discuss
possible reasons for this discrepancy, with the most likely conclusion being
target selection and Eddington bias.
