Sherryl,
Statutory recording of births only started in Ireland in 1864. Prior to that you are reliant on church records, where they survive. You don?t say what denomination William and Eliza were, and this is essential to help identify the correct records.
A research tool in Ireland called Griffiths Valuation lists most farmers in the mid 1800s. The records for the Strabane area were compiled in 1858. There is only 1 William Day listed in the whole county. He was living on plot 8a in a townland called Killyclooney. He had a farmhouse, outbuildings and a one third share of 74 acres of land. He shared with Isabella Hunter & John Bailey. William?s farm today is on the Killycurry Rd, about 12 miles north east from Strabane.
I do not know that this is your William. All I can say is that he was apparently the only William Day farming in Co Tyrone in 1858.
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=nameS…
Death registration only started in Ireland in 1864 and so if William died before that it won?t be recorded in the statutory registers. For deaths registered in Strabane 1864 ? 1900 there is only one for a William Day. He died in 1872 (Strabane, Volume 7, page 251) and had an estimated year of birth of 1786. Possibly the William from Killyclooney. (You can order a photocopy of that death cert from GRO Roscommon. Should cost ?4). http://www.groireland.ie/
Looking at the 1901 census, I see 2 households in Killyclooney with Days in them. The first is probably the same farm as is listed in Griffiths Valuation, the other is probably a relation to the first:
http://www.census.nationalarchives.ie/pages/1901/Tyrone/Dunnamanagh/Kil…
http://www.census.nationalarchives.ie/pages/1901/Tyrone/Dunnamanagh/Kil…
I noted one probate file for this family. Only the abstract (summary) is on-line. The will and any supporting documents should be held in PRONI (the public record office) in Belfast.
Full Abstract :
Day William of Killyclooney county Tyrone farmer died 4 August 1928 Probate Londonderry 15 May to Robert Allen farmer. Effects ?12 19s. 1d.
The family were evidently Presbyterian. Assuming Elizabeth Day was also Presbyterian, and you have no other leads as to where she came from, you might want to investigate the baptismal and marriage records for Presbyterian churches in that area to see if she is listed. Few of those church records are on-line. However most have been copied and are on microfilm in PRONI, Belfast.
Another set of records to check would be the tithe applotment records for Co Tyrone. These (compiled for tax raising purposes) list people with land. So again every farmer would normally be listed. They cover the period 1820/1830. Those for Co Tyrone are not on-line but again copies are held in PRONI. You can check Killyclooney to see if William was farming there then, and also look for any other William Days elsewhere in Co Tyrone.
Finding Nancy Ash without her father?s name or occupation will be tricky. She likely came from the same area as her husband though. In those days you generally married someone near to where you lived. Looking at the 1901 census, there are only 9 people named Ash in Co Tyrone. One of them was an Andrew Ash who was a servant in Killyclooney, the same townland that William Day lived in, and apparently in the house next door to the Day farm. That?s quite a coincidence and would make you think it must be the right family. However I note that this Andrew Ash was born in Co Donegal and so probably his family didn?t originate in the Killyclooney area. He was also RC. I don?t suppose you know whether Nancy was also RC?
http://www.census.nationalarchives.ie/pages/1901/Tyrone/Dunnamanagh/Kil…
Elwyn