When we draw the lewis structure for [CO3]^2- , we get a double bond between one oxygen and the carbon, with single bonds between the other two oxygen atoms and the carbon. Because each of the oxygens want a double bond to the carbon, they all fight over it (giving resonance structures), meaning that in the end, you get a bond something between a double and a single bond for each Carbon-Oxygen bond. Therefore, this bond will be longer than a single bond, but shorter than a double bond.