A method of producing a CMC article having a net shape, and by which the article can be formed to have an exterior surface with desirable characteristics, such as being free of an imprint pattern of a fiber reinforcement material within the article. The method entails providing a body comprising the fiber reinforcement material, and depositing a coating on a surface of the body. The coating contains a carbonaceous binder and a slurry containing a ceramic particulate material. Following its deposition, the carbonaceous binder within the coating is cured to render the coating machinable, and the coating is then machined to approximately produce the net shape of the article.