Many head-stones only show the year of death, not the full date. Others may record the internment date rather than date of death.
Where would I locate more accurate dates of death before the 1800's in the US?
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Disclaimer: I haven't done much research in the period, but these are the questions I would ask and attempt to answer if I were looking to confirm a death date for a pre-1800 tombstone.
When records are scanty, look at everything you can think of (not just the records that you think will have a date of death) because it's impossible to tell which one of those records might hold a clue that will lead you to a record which does have the death date.
Very, very occasionally, luck will smile upon you and the records of the doctor who attended the family will have survived in a repository somewhere (a society, a library, an archive). If not published in book form, perhaps a transcription is available in a genealogical or historical journal.