To determine the magnetic behaviour, we evaluate the number of unpaired electrons in the central metal ion of each complex :

1. $[Ni(CN)_4]^{2-}$: The central metal ion is Ni in the +2 oxidation state with a $3d^8$ configuration. Since $CN^-$ is a strong field ligand, it causes the pairing of the two unpaired $3d$ electrons against Hund's rule. This results in zero unpaired electrons ($n=0$), making the complex diamagnetic .
2. $[CuCl_4]^{2-}$: The central metal ion is Cu in the +2 oxidation state ($3d^9$). It has one unpaired electron, making it paramagnetic.
3. $[CoF_6]^{3-}$: The central metal ion is Co in the +3 oxidation state ($3d^6$). $F^-$ is a weak field ligand and does not pair the electrons, leaving 4 unpaired electrons. It is paramagnetic .
4. $[NiCl_4]^{2-}$: The central metal ion is Ni in the +2 oxidation state ($3d^8$). $Cl^-$ is a weak field ligand, so the pairing of electrons does not occur, leaving 2 unpaired electrons. It is paramagnetic .

Therefore, $[Ni(CN)_4]^{2-}$ is the diamagnetic complex.