I'm playing on Noble level and several times I've wanted to offer to declare war on a computer civ, helping another computer civ out, but I never have any civs under the Declare War option in my diplomacy column. Why is this?

Because if that option had been included in the game, it could (and would) be easily abused by humans. So they just left the heading of "Declare War On..." there, but you can never use it.

Are you serious? I can actually never use it?

You could just declare war yourself. You'd still get the "mutual military struggle" diplomacy boost.