If the Dunseith family was Presbyterian then that indicates Scottish origins. The vast majority of Scots settlers arrived in Co Antrim (and other parts of Ulster) in the 1600s. Presbyterian is the most common denomination in Co Antrim because majority of the population in that county are descendants of Scots settlers. (Known as Scots-Irish in North America and Ulster-Scots in Ireland). If Sarah said her parents were born in Ireland then I’d be inclined to believe that, as she was more likely to know than the informant for her death certificate. Mistakes on death certificates are common. Her daughter probably was aware there was a Scottish connection somewhere and guessed Sarah’s parents place of birth but, in my opinion, the link to Scotland would have been several generations further back in time.
Death registration started in Ireland in 1864. Looking at the deaths in Co Antrim 1854 to 1920, I can see several of men old enough to be Sarah’s father, notably around Ballymena and Randalstown. But without more information eg a mother’s name and William’s occupation it’s not possible to say which, if any, is the right one.
A birth around 1844 is well before the start of birth registration in Ireland (again 1864) and so you need to rely on church baptism records. Not all churches have records for 1844 and of those that do, not all are on-line. However where they survive, they are in PRONI (the public record office) in Belfast. A personal visit is required to view them. If you get no other leads, you might want to visit PRONI and search the Presbyterian records in and around Ballymnea.
If you could find Sarah’s marriage to William Craig, then that might give a mother’s name which would help a lot.
I can see a gravestone for William Dunseath in Clough graveyard (north of Ballymena). No date or further information on it. Also this in Grange Presbyterian churchyard near Randalstown:
Erected by DAVID DUNSEATH, GILLISTOWN. In Memory Of His Father WILLIAM DUNSEATH, Who Died 28th November. 1895. Aged 87 Years. Also His Mother ESTHER DUNSEATH, Who Died 11th January, 1892. Aged 81 Years. And His Wife MARGARET DUNSEATH, Who Died 13th April, 1935. Aged 89 Years. Also The Above Named DAVID DUNSEATH, Who Died 4th May. 1938. Aged 86 Years.
Possibly DNA testing may be a way of matching with others who have additional information about where the family originate. Family Tree DNA reportedly has more people with Ulster roots than any other company. That obviously increases the chances of finding a match. You might want to try them or, if you have already tested, you can transfer your results to them for no fee.
The North of Ireland Family History Society is running an Ulster DNA project in conjunction with FTDNA and can offer testing kits at a reduced price. http://www.nifhs.org (Go to DNA project on the website).