Qualifications
In many rural states, you don't need a medical license—or even any medical training, for that matter—to be a coroner.
However, if you want to be valuable in places where you're not related to half the population, you might want to consider medical school. Sure it's eight years of schooling, MCATs, and a whole lot of math and science—but hey, if you get tired of working on dead people, at least you have a different career to fall back on.
At the very least you'll want a B.S. in anatomy, pathology, or forensic science (with a bit of criminology thrown in) to be any good at this job.