Can you carbonate a non aqueous liquid?
$\ce{CO2}$, being non-polar (due to the 180 degree bond angles),  will probably be more soluble in solvents that are non-polar as well, although the quadrupole moment might cause higher solubility in polar solvents as well (thanks to @georg for this addition). Also temperature will play a significant role, the higher the temperature the lower the solubility. 

These qualitative remarks however only take you so far. If you really want to know the solubility in a specific liquid you will have to look it up or, if that is not possible, test it yourself. In this paper they test the solubility of $\ce{CO2}$ in different types of crude oil and make predictions based on the structure of the oil.

I cannot find anything specific for corn oil, although the reverse process of dissolving palm oil in supercritical $\ce{CO2}$ might set you on the right track to find what you want to know.

Just a fun addition: don't ever try to carbonate milk as these guys do - it will get messy! (it is in Dutch, but you can still watch what happens). Click here an English video with similar footage