Kathleen,
Statutory birth registration didn’t start I Ireland till 1864. Prior to that you have to rely on church records. I assume the family was Roman Catholic. The majority of Daly/Daily/Dailey households in the 1901 Irish census of Tyrone were RC, but they weren’t all so it’s important to know. Otherwise you may be looking for the wrong records. There were a total of 628 people of that name in the county then.
Beragh is in the civil parish of Clogherny (RC parish of Ballintacker). Drumnakilly is in the parish of Termonmaguirk (RC parish of Termonmacguirk). The two are immediately beside each other and, unusually, part of Cloghenry is in the middle of Termonmaguirk. There’s a map here which shows the relationships:
https://www.ancestryireland.com/civil-parish-maps-for-ulster/civil-parishes-of-county-tyrone/
So the two are close together.
Termonmacguirk’s RC records start in 1834 and Ballintacker in 1832, so both are too late for someone born in 1824. The RC parish records are on-line free on the National Library site:
https://www.nli.ie/en/family-history-introduction.aspx
There were 10 Daly/Daily/Daley households in Drumnakilly in 1901 (out of a total of 57 houses):
http://www.census.nationalarchives.ie/pages/1901/Tyrone/Drumnakilly/Drumnakilly/
They were all farmers or cottiers (small farmers). Some of them will likely be related to each other. Ignore the variations in spelling. Accurate spelling was not something that troubled the average person in Ireland in the 1800s and early 1900s and it varies all the time, often according to the whim of the person recording the information. Much of the population then wasn’t very literate and often neither knew nor cared how their named was spelled in church or other records.
The tithe applotment records were compiled over a period of years in the 1820s and 1830s. They list people with land (the tithe was a tax on land). The records for Termonmaguirk were compiled in 1825. Drumnakilly was spelled Drumnakillagh in those records, and Daily etc was spelled in various different ways including Dawley. There look to have been 4 Dawley (Daily) farms in Drumnakilly then.
https://cotyroneireland.com/tithe/termonmaguirk.html
Just 1 Daley farm in Clogherny parish. He was Nale (ie Neil) in Clogherny Slave townland. (Clogherney Slave is from the Irish meaning stony place. Nothing to do with slavery). No Daley in Beragh itself. That doesn’t mean your family don’t come from Beragh, merely that they probably didn’t have any significant quantity of land. So like much of the population they were probably labourers/weavers or in other trades that didn’t involve owning or renting a farm. (Most people in rural areas would have a few perches to grow potatoes but that wasn’t significant enough to make it into the tithes). A perch is a one hundred and sixtieth part of an acre.
https://cotyroneireland.com/tithe/clogherny.html
If there’s no sign of the family in the parish records (eg later children born after the records begin) there’s probably not much that can be done by way of tracing them, apart from looking for gravestones. RC churches didn’t keep burial records. Farmers were a bit better off than the rest of the population and often had gravestones. Most labourers were buried without one. Statutory death registration didn’t start till 1864 so I would think John Daily born 1787, and his wife were probably dead before that.
The surname McGurvie isn’t common, but I did notice 2 McGarveys in Termonmaguirk’s tithes. So that might be the name. There were still some McGarveys farming in Torsallagh in 1901:
http://www.census.nationalarchives.ie/pages/1901/Tyrone/Athenree/Tursallagh/1747790/
A problem you face in tracing living descendants of someone who left Ireland in the 1840s or 1850s, especially with a common name like Daily, is that the average family here probably only knows their ancestry back about 3 generations, so perhaps to around 1900. Most wouldn’t know what ancestors they had born in 1787 or 1824. You’ll have to hope to get lucky and find a family that knows a bit more.
Beragh is easy enough to find so I won’t both with any directions. If you are looking for Drumnakilly or Torsallagh/Tursallgh, then it’s on the B4 road between Omagh and Carrickmore. There’s a village and then that’s surrounded by 1352 acres of land all of which forms part of the townland. Tursallagh is much smaller. The centre is at the intersection of the Tursallagh and Maginn Roads, a few miles eats of Sixmilecross.
