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Honestly, you'll probably do better (make money in the process) by selling your manual C6 and buy an automatic.
Manual transmissions are rarer than the automatics, and more desired by many Corvette fans (especially the ones who drive them competitively). That means they generally command a higher selling price than a similarly optioned C6 with an automatic transmission.
Unless you have a strong emotional (irrational) attachment to the exact C6 you have now, I wouldn't try to convert manual to automatic. It would be an expensive conversion (easy to see it costing in the $5K to $10K range, all included), and would devalue the car you have now.
It has been done before, but I agree that I would personally sell and buy an automatic, to avoid all the cost and potential troubles that could happen with the swap.