As a COD driver, I'll let you in on a little secret. IF (big one there) the C-2B is made, it will have the capability to be a tanker. As it is now, we can carry 10,000 lbs in our cage (9914 lbs with internal fuel tanks). If the B variant were indeed to have extra range as "planned" then we should be able to loiter longer above the ship with more fuel. I understand the idea that the C-2 is not organic to the ship. I agree; even though we are part of the air wing now, we still spend a lot of time operating from the beach. However, that is not to say that a C-2 could not fulfill the role as a tanker. Obviously I don't know what speed most refueling takes place at, but it's not like the COD putts around at 120 kts. If need be, we can pick it up (a little).
All of that being said, you are really compromising the mission of the C-2 if you want it to be a tanker too. For DV missions alone we require using both CODs (one as a turning spare). I can't imagine any CAG wanting to use a COD as a tanker.