Forty molecular cloud cores in the southern hemisphere from the initial Spitzer Space Telescope Cores-to-Disks ( c2d ) Legacy program source list have been surveyed in ^ { 13 } CO ( 2 \rightarrow 1 ) , ^ { 12 } CO ( 4 \rightarrow 3 ) , and ^ { 12 } CO ( 7 \rightarrow 6 ) with the Antarctic Submillimeter Telescope and Remote Observatory ( AST/RO ) . The cores , ten of which contain embedded sources , are located mostly in the Vela , Ophiuchus , Lupus , Chamaeleon , Musca , and Scorpius complexes . ^ { 12 } CO ( 7 \rightarrow 6 ) emission was undetected in all 40 clouds . We present data of 40 sources in ^ { 13 } CO ( 2 \rightarrow 1 ) and ^ { 12 } CO ( 4 \rightarrow 3 ) , significant upper limits of ^ { 12 } CO ( 7 \rightarrow 6 ) , as well as a statistical analysis of the observed properties of the clouds . We find the typical ^ { 13 } CO ( 2 \rightarrow 1 ) linewidth to be 2.0 km s ^ { -1 } for cores with embedded stars , and 1.8 km s ^ { -1 } for all others . The typical ^ { 12 } CO ( 4 \rightarrow 3 ) linewidth is 2.6 to 3.7 km s ^ { -1 } for cores with known embedded sources , and 1.6 to 2.3 km s ^ { -1 } for all others . The average ^ { 13 } CO column density derived from the line intensities was found to be 1.9 \times 10 ^ { 15 } cm ^ { -2 } for cores with embedded stars , and 1.5 \times 10 ^ { 15 } cm ^ { -2 } for all others . The average kinetic temperature in the molecular cores , determined through a Large Velocity Gradient analysis of a set of nine cores , has an average lower limit of 16 K and an average upper limit of 26 K. The average molecular hydrogen density has an average lower limit of 10 ^ { 2.9 } cm ^ { -3 } and an average upper limit of 10 ^ { 3.3 } cm ^ { -3 } for all cores . For a different subset of nine cores , we have derived masses . They range from 4 to 255 M _ { \odot } . Overall , our c2d sample of southern molecular cores has a range of properties ( linewidth , column density , size , mass , embedded stars ) similar to those of past studies .