frek,
I think Diddy and Steve have covered your options.
Within the "ancient" Parish of Earsdon ( Seaton Sluice-formerly Hartley Harbour, lay within Hartley, one of the eight "townships" that made up Earsdon Parish) there were several burial places.
From early times the church graveyard of the Parish Church of St Albans was the burial site for folk within the parish.
Then from about 1849 the church graveyard of the Holy Trinity of Seghill ( Seghill was another of Earsdon Parish's "townships") was available.
St Cuthberts of Blyth was a "chapel of ease", a satellite of the parish church at Earsdon. And it's small graveyard was used from 1859 to 1864.
Then Blyth Civil cemetery was established from about 1860. Known as Links Cemetery.
Both of the above two sites in Blyth ( the southern part of today's Blyth) lay in the "township" of Newsham, another of Earsdon parish's "townships".
Although within the bounds of Earsdon Parish, there were several churches of other religious denominations, I don't think any had their own graveyards. ( The RC graveyard of St Cuthberts, Cowpen lay within the parish area of Horton).
So I think your deaths in 1851 and 1856 are going to be in St Albans or Holy Trinity. Ditto for the next three deaths, plus Blyth Links cemetery.
These burial records accessible in Northumberland County record Office (Woodhorn), Tyne & Wear Archives (Newcastle) and Newcastle City Library and other places (e.g. Blyth Library).
What were your folks names ?
Michael Dixon