Diamagnetic species are those which have all their electrons paired.
In [Ni(CN)$_4$]$^{2-}$, nickel is in the +2 oxidation state with a fully paired electron configuration, making it diamagnetic.
The other complexes, such as [NiCl$_4$]$^{2-}$, [Fe(CN)$_6$]$^{3-}$, and [CoF$_6$]$^{3-}$, have unpaired electrons and are thus paramagnetic.