$\left[\mathrm{Mn}(\mathrm{CO}{)}_4\mathrm{NO}\right]$ is diamagnetic because :

$$\begin{gathered} \left[{\stackrel{+1}{\mathrm{Mn}\left(\mathrm{CO}\right)}}_4\left({\mathrm{NO}}^{-}\right)\right]:\text{Paramagnetic due to presence of unpaired }{\mathrm{e}}^{-}\mathrm{s}\text{ in }{\mathrm{NO}}^{-} \\ \left[\mathrm{Mn}(\mathrm{CO}{)}_4\left({\mathrm{NO}}^{+}\right)\right]:\text{No unpaired }{\mathrm{e}}^{-}\text{either on ligands or on }\mathrm{Mn}\text{ hence it is diamagnetic } \end{gathered}$$