Does the carbon dioxide dianion exist?
The obvious Star Wars puns aside, I have never heard about the dianion of a carbon dioxide dianion and/or that it was named carbonite.
However, the carbon dioxide radical anion, $\ce{CO2^{.-}}$, is experimentally available.
Typically, it is generated by hydrogen atom abstraction from formate, $\ce{HCOO-}$, using $\ce{HO^.}$ radicals. The $\ce{HO^.}$ radicals, in turn, are obtained from vacuum ultraviolet (VUV) irradiation of water at a wavelength of $\lambda = 175~\mathrm{nm}$.

UPDATE
Apparently, I was wrong about the dianion! As Mithoron pointed out in his comment, species like $\ce{(M^+)_2CO2^{2-}}$, formed in the reaction carbon dioxide with alkali metals in argon or nitrogen matrixes, have been detected by IR spectroscopy. See Inorganic Chemistry, 1984, 23, 177-184 for details.