The majority of pre 1858 wills were destroyed in Dublin in 1922, in a fire during the Irish civil war. Only a small number survived, though indexes did survive from which we can sometimes find details of when a will was probated, even though the document itself is lost. You can search for pre 1858 wills for Co Derry on this site. However I don’t see one for John who died in 1809.
Many wills didn’t need probate in those days and so a lot never made it into official records anyway.
The death is long before the start of statutory records in Ireland (1864) and so you won’t get a death certificate for John.Fe w records have survived from that period and it will be very difficult to find any documentary evidence relating to John. If he was Church of Ireland then there might be a burial record (if you know where he was buried) but most other denominations do not keep burial records.
When you say John was thought to be born in Londonderry, do you mean the city or the county? Do you know what denomination he and Martha Love were, and where they married or lived?