I don't have any personal experience with stains on carbon but try some car wax and a microfiber cloth. I have a feeling that would work (if it doesn't remove the car wax with rubbing alcohol so it doesn't coat over it making it harder to remove). Another thing to try could be WD40... and if all else fails try Mr. Clean eraser cleaning pads (basically a 2200+ grit wet sponge).
seriously, carbon is pretty tough. Even the resin is not easily broken down. Remember this is a space age material. In fact, its so tough to break down that there is no real way to recycle it. Most of it just gets landfilled. So most solvents won't really hurt the carbon at all. Now the paint is another story.