Definition of a homoleptic complex

A homoleptic complex is a coordination compound in which the central metal ion is bonded to only one kind of ligand.

If more than one type of ligand is present, the complex is heteroleptic.

Check each option

Option A: $\left[\mathrm{Ni}\left(\mathrm{NH}_3\right)_2 \mathrm{Cl}_2\right]$

• Ligands present: $\mathrm{NH}_3$ and $\mathrm{Cl}^-$
• Two different kinds of ligands are present.
• So, this is heteroleptic.

Option B: $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}_2\right]^+$

• Ligands present: $\mathrm{NH}_3$ and $\mathrm{Cl}^-$
• Two different kinds of ligands are present.
• So, this is heteroleptic.

Option C: $\left[\mathrm{Fe}\left(\mathrm{NH}_3\right)_4 \mathrm{Cl}_2\right]^+$

• Ligands present: $\mathrm{NH}_3$ and $\mathrm{Cl}^-$
• Two different kinds of ligands are present.
• So, this is heteroleptic.

Option D: $\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}$

• Ligands present: only $\mathrm{CN}^-$
• Only one kind of ligand is present.
• So, this is homoleptic.

Conclusion

The homoleptic complex is: $\boxed{\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}}$

Hence, the correct option is D.