I need to have someone do animation work for an iOS game I'm developing (using cocos2d), however this person does not have a Mac and as such cannot run Xcode.
Is there a way for them to create animations for me without the use of Xcode?
No, if you are referring to writing Objective-C using the Cocos2D framework to do animations, your animator will not be able to do so without xCode. He could write the code in a text file and pass that to you, but will not be able to compile them to check that they do work (which really defeats the purpose I suppose.)
However, if you only need sprite animations then the person can create the sprite animation using flash or some such software (then export the PNG of each frame for you.) Then you can use those animation frames in your app.