  Using the Australia Telescope Compact Array (ATCA), we conducted a survey of
CO J=1-0 and J=2-1 line emission towards strongly lensed high-redshift dusty
star forming galaxies (DSFGs) previously discovered with the South Pole
Telescope (SPT). Our sample comprises 17 sources that had CO-based
spectroscopic redshifts obtained with the Atacama Large
Millimeter/submillimeter Array (ALMA) and the Atacama Pathfinder Experiment
(APEX). We detect all sources with known redshifts in either CO J=1-0 or J=2-1.
Twelve sources are detected in the 7-mm continuum. The derived CO luminosities
imply gas masses in the range (0.5-11)x10^{10} M_sun and gas depletion
timescales <200 Myr, using a CO to gas mass conversion factor alpha_CO=0.8
M_sun (K km/s pc^2)^{-1}. Combining the CO luminosities and dust masses, along
with a fixed gas-to-dust ratio, we derive alpha_CO factors in the range
0.4-1.8, similar to what is found in other starbursting systems. We find small
scatter in alpha_CO values within the sample, even though inherent variations
in the spatial distribution of dust and gas in individual cases could bias the
dust-based alpha_CO estimates. We find that lensing magnification factors based
on the CO linewidth to luminosity relation (mu_CO) are highly unreliable, but
particularly when mu<5. Finally, comparison of the gas and dynamical masses
suggest that the average molecular gas fraction stays relatively constant at
z=2-5 in the SPT DSFG sample.
