The incorrect statement about carbonate $\left({\mathrm{CO}}_3^{2-}\right)$ ion is,

Resonating structure of carbonate ${\mathrm{CO}}_3^{2-}$ ion are

In resonating structures bonds are not fixed and therefore, all bond lengths are equal.

The hybridisation of central atom is ${\mathrm{sp}}^2$.

Thus, there is no coordinate bond present in ${\mathrm{CO}}_3^{2-}$. Hence, the second statement is incorrect.