  We present spatially-resolved imaging obtained with the Australia Telescope
Compact Array (ATCA) of three CO lines in two high-redshift gravitationally
lensed dusty star-forming galaxies, discovered by the South Pole Telescope.
Strong lensing allows us to probe the structure and dynamics of the molecular
gas in these two objects, at z=2.78 and z=5.66, with effective source-plane
resolution of less than 1kpc. We model the lensed emission from multiple CO
transitions and the dust continuum in a consistent manner, finding that the
cold molecular gas as traced by low-J CO always has a larger half-light radius
than the 870um dust continuum emission. This size difference leads to up to 50%
differences in the magnification factor for the cold gas compared to dust. In
the z=2.78 galaxy, these CO observations confirm that the background source is
undergoing a major merger, while the velocity field of the other source is more
complex. We use the ATCA CO observations and comparable resolution Atacama
Large Millimeter/submillimeter Array dust continuum imaging of the same objects
to constrain the CO-H_2 conversion factor with three different procedures,
finding good agreement between the methods and values consistent with those
found for rapidly star-forming systems. We discuss these galaxies in the
context of the star formation - gas mass surface density relation, noting that
the change in emitting area with observed CO transition must be accounted for
when comparing high-redshift galaxies to their lower redshift counterparts.
