In the case of a suicide, or any other violent death, an inquest will have been held, and in the past this might well  in the nearest public house, within a day of the death (before the body started to smell). After 1837 the cause of death will be given on the death certificate. There could be a report in a local newspaper  such as the case of William Wood in 1828 or  John Olliffe in 1827. Such reports are more likely later in the 19th century after the stamp tax came off and the size of papers started to increase. However few local papers are indexed - and while the HALS index contains some index cards relating to newspaper articles it probably covers less than 1% of what would be necessary for a reasonably comprehensive index.

When I recently asked about a particular inquest I discovered that in many cases the coroner's records will not have survived - although there will be Court records in the case of a murder - when the culprit is tried.

Basically your best advice is to work out the family tree properly - and (assuming you are talking after 1837) track down the deaths of likely candidates. Then buy their death certificates which will give the cause of death. If they committed suicide, or there was some other reason for an inquest. you now have a precise date to look at the relevant newspaper.

Other Examples

A Fatal Road Traffic Accident in St Albans - 1885

Shocking Death of a Game-Keeper at Bell Bar - 1890

SAUNDERS, Aldbury, inquest in 1882