Which of the following diatomic molecular species has only π bonds...

{C}_{2} = $\left(12\right);$ $\sigma1{s}^{2} < \overset{*}{\sigma}1{s}^{2} < \sigma2{s}^{2} < \overset{*}{\sigma}2{s}^{2} < \pi2{p}_{x}^{2} = \pi2{p}_{y}^{2}$

So according to MOT, the orbitals involved in bonding are only pie orbital.

Hence ${C}_{2}$ contains only $\pi$ bonds.