My cat's cold won't go away. He has green mucus and a cough.

Poor Romeo! Cats are prone to upper respiratory infections that can cause the symptoms you are describing. These are often viral, but can be mixed with bacterial infections as well. Stress reduction and proper ventilation can sometimes help in these cases. Cats need at least one litterbox per cat plus one extra to help reduce stress associated with the litterbox. They should be placed in separate rooms, away from the food and water bowls, must be scooped at least daily (preferably multiple times a day)and washed out at least weekly with a mild soap, followed by thorough rinsing. Cats need a lot of space to explore, but keeping them indoors is much safer than letting them outside, due to the risk of injury from cars, wildlife, other animals, etc. The key is providing space (particularly vertical space for climbing, such as cat trees, ledges, and the like) inside the home. Visit http://www.veterinarypartner.com/Content.plx?P=T&C=33&S=2 and https://indoorpet.osu.edu// for tips on stress reduction. Also look into Feliway, a synthetic pheromone that is available in a diffuser and spray form that promotes calm feelings in cats http://www.feliway.com. In some cases, persistent nasal discharge can be causes by a polyp, mass or foreign object stuck in the nose, which would require further veterinary care. Your vet may recommend imaging to see if there is anything visible in the nose that could be causing this. If you notice Romeo having difficulty breathing, exercise intolerance, or pale gums, have him seen by a vet right away, as this can be dangerous respiratory distress. God luck to you both!