One version says the term comes from the French word "conasse". During the Second World War, many Cajun men served in the armed forces. When in France, many of the French heard the Cajuns speaking in a French that was both very old and in a French that had some very odd words. The Frenchmen called the Cajuns "conasse" which translates to a very low-grade prostitute. I would think this comes from the fact that, although they spoke a form of French, the Cajuns weren't real Frenchmen.
Of course, the "American" servicemen heard "conasse" as "CoonAss". In a world where "RedNeck" is heard often, "CoonAss" fits right in. Just like RedNeck, it wasn't originally used as a term of endearment. But many Cajuns carry it as a description of themselves as good as any other. In Louisiana, you can find vehicles with bumper stickers reading "Registered CoonAss" or "I'm a CoonAss, Me!" Wide spread use came about during the oil boom in Louisiana during the 60's and 70's.
But there is very little to prove or disprove that version.