Step 1: Recall the property of coordination compounds.
Coordination compounds are mainly formed by transition metal ions because they have vacant d-orbitals available for coordination with ligands.
Step 2: Analyze each ion.
- (A) Na$^{+}$: Belongs to group 1 (s-block). It has no vacant d-orbitals and does not form coordination compounds.
- (B) Cr$^{2+}$: Transition metal ion, forms complexes (e.g., [Cr(H$_2$O)$_6$]$^{2+}$).
- (C) Co$^{2+}$: Transition metal ion, forms complexes (e.g., [Co(NH$_3$)$_6$]$^{2+}$).
- (D) Cr$^{3+}$: Transition metal ion, forms complexes (e.g., [Cr(H$_2$O)$_6$]$^{3+}$).
Step 3: Conclusion.
Only Na$^{+}$ does not form coordination compounds because it lacks d-orbitals.
\[
\boxed{\text{Na}^{+}}
\]