It seems like learning a language following the same process as learning your mother tongue makes sense, no matter your age. And that natural process (hear and speak, then read and write) has been emphasized by older students/adults around me. For example, I know several adults who studied a foreign language for a couple of years in high school, using the usual means of learning from a book and doing reading and writing along with some speaking, but they barely remember any of it. Other adults I know went on a mission trip to a foreign country and were immersed in the language, mainly hearing it, for six weeks. During that time they could pretty well follow a conversation and were beginning to speak the language a bit themselves.
So I would think that the CM-recommended way to learn languages would hold true, no matter how old the student may be.
Does your library have any children’s books on tape in Spanish? Especially if the story were a familiar tale, you could put up the book and just have your student listen to the Spanish audio. The library might also have some documentaries or other video projects that can be listened to in Spanish. Ideally, you might be able to find a person who speaks fluent Spanish. Even if that person lives elsewhere, you could use Skype or some other technology to connect your student with a native speaker.
Just a few ideas that popped into my head. Maybe others can contribute more . . .