  We present observations of CO J=2-1 line emission in infrared-luminous
cluster galaxies at z~1 using the IRAM Plateau de Bure Interferometer. Our two
primary targets are optically faint, dust-obscured galaxies (DOGs) found to lie
within 2 Mpc of the centers of two massive (>10^14 Msun) galaxy clusters. CO
line emission is not detected in either DOG. We calculate 3-sigma upper limits
to the CO J=2-1 line luminosities, L'_CO < 6.08x10^9 and < 6.63x10^9 K km/s
pc^2. Assuming a CO-to-H_2 conversion factor derived for ultraluminous infrared
galaxies in the local Universe, this translates to limits on the cold molecular
gas mass of M_H_2 < 4.86x10^9 Msun and M_H_2 < 5.30x10^9 Msun. Both DOGs
exhibit mid-infrared continuum emission that follows a power-law, suggesting
that an AGN contributes to the dust heating. As such, estimates of the star
formation efficiencies in these DOGs are uncertain. A third cluster member with
an infrared luminosity, L_IR < 7.4x10^11 Lsun, is serendipitously detected in
CO J=2-1 line emission in the field of one of the DOGs located roughly two
virial radii away from the cluster center. The optical spectrum of this object
suggests that it is likely an obscured AGN, and the measured CO line luminosity
is L'_CO = (1.94 +/- 0.35)x10^10 K km/s pc^2, which leads to an estimated cold
molecular gas mass M_H_2 = (1.55+/-0.28)x10^10 Msun. A significant reservoir of
molecular gas in a z~1 galaxy located away from the cluster center demonstrates
that the fuel can exist to drive an increase in star-formation and AGN activity
at the outskirts of high-redshift clusters.
