  We report on a scheme for laser cooling of $^{12}$C$_2$. We have calculated
the branching ratios for cycling and repumping transitions and calculated the
number of photon scatterings required to achieve deflection and laser cooling
of a beam of $C_2$ molecules under realistic experimental conditions. Our
results demonstrate that C$_2$ cooling using the Swan ($d^3\Pi_\text{g}
\leftrightarrow a^3\Pi_\text{u}$) and Duck ($d^3\Pi_\text{g} \leftrightarrow
c^3\Sigma_\text{u}^+$) bands is achievable via techniques similar to
state-of-the-art molecular cooling experiments. The Phillips ($A^1\Pi_\text{u}
\leftrightarrow X^1\Sigma_\text{g}^+$) and Ballik-Ramsay ($b^3\Sigma_\text{g}^-
\leftrightarrow a^3\Pi_\text{u}$) bands offer the potential for narrow-line
cooling. This work opens up a path to cooling of molecules with carbon-carbon
bonds and may pave the way toward quantum control of organic molecules.
