First of all, a coroner is in many areas an elected official, (or appointed by mayors, governors and the like, depending on the state) and there are more coroners out there than you would guess who do not have a medical degree at all. Salaries vary greatly depending on the area.
However, assuming you mean coroner as in a forensic pathologist (what most people think of...doing autopsies, working with police, etc.) you need to get a pathology residency, in which you do all aspects of pathology (doing autopsies is one specialized area within pathology, others include surgical pathology, cellular pathology...). Then do a subinternship or fellowship in the subspecialty of forensic pathology. I may not be completely accurate about this, but this is the gist of what my pathology instructor told us.
I know pathology is one specialty that needs people, so the pay is probably pretty good...you can look these up online somewhere. I don't know about forensic pathology specifically though (my guess is that it is a more popular subspecialty area, so wages may be lower than other types of pathologists).