Hi Barbara,
I've not had experience with obtaining coroners' records, but I was able to obtain a newspaper article reporting on the inquest of an ancestor, by contacting the local records centre (Lambeth, south London) and asking which papers would be most likely to have the information. They were then able (for a small fee) to provide me with copies of the article. I was also lucky enough to find three articles in the Times Digital Archive (website - I don't have the ref right now) about the death, because it was caused by an explosion and subsequent house fire.
I would recommend contacting the records centre relevant to the place of death, and seeing what they have.
Hope this helps
Prue