I'm not a coroner, but as part of my job, I have to find good health-related systems.
I would definitely say that emorgue.com is the best coroner/morgue case management system.
Really fast and a great UI. I didn't need any kind of help or tutorial to use. Customizable sections and employee management was great.
It had a free account, but I used premium. I didn't pay anything yet but it seems low price (23$) for a premium software. I did test two others. To use both others, I had to contact people directly so they would let me test their software.