How to rationalise the increasing bond length order in the carbonate ion, carbon monoxide, and carbon dioxide?
Actually, in regard to bond length, you should be looking at the bond order of a single bond within the molecule. The bond order is 2, not 4, for $\ce{CO2}$, and the bond order for the carbonate ion is somewhere between 1 and 2 due to resonance. Thus, the carbonate ion has the longest bond length, followed by carbon dioxide, and finally carbon monoxide.