Definitely shoot it in the head, as others have said.
Regarding CO2: I believe it depends on the concentration. At very high levels, it's more humane, since it has an asphyxiating effect, similar to an inert gas such as nitrogen, but at lower levels, it causes a feeling of drowning, which is much more unpleasant.
What are you going to do with the carcass?
If it's disease free, I would eat it. Obviously I'd make sure it's very well cooked and I wouldn't sell the meat for a profit, but give it to friends and family. Dog food can be made from part people don't want to eat and the bones can be ground to make bonemeal for the garden. I would feel more comfortable eating a wild animal, than one from a large farm where it has been pumped full of hormones and antibiotics.
If it was diseased, then I'd either burn it, or dig a very deep hole and bury it. It would be expensive to pay someone to dispose of it for you.
Oh and one important thing is: don't eat the brain and spinal cord as they can harbour nasty prion diseases which don't get destroyed by cooking.