In [NI(CN)4]2-, Ni is in +2 oxidation state with electronic configuration = 384so.
Cl- is a weak ligand. It cannot pair up the electrons in 3d orbitals. Hence, it is paramagnetic. In [Ni(CO)4], Ni is in zero oxidation state and its configuration is -3d84S2 . In the presence of CO ligand the 4s electrons shift to 3d orbital to pair up the 3d electrons. Thus, there is no unpaired electron present. Hence it is diamagnetic.