Statutory birth, death and marriage registration (in some jurisdictions called Vital Records) only started in Ireland in 1864, save for non RC marriages which were recorded from 1845 onwards. So you probably won’t find statutory birth, death or marriage certificates in Ireland for this family. For earlier years you usually need to rely on church records, where they exist. Ideally you need to know the precise denomination and have some idea of where the person was born in order to search the correct records. Not all churches have records for that period and not all that do are on-line.
RC records are mostly on-line on the nli site:
https://www.nli.ie/en/family-history-introduction.aspx
For other denominations, the churches usually hold the originals but there are also copies in PRONI, the public record office, in Belfast. A personal visit is required to access them. Access to the records there is free. This link explains what records exist, parish by parish:
https://www.nidirect.gov.uk/publications/proni-guide-church-records
If you are unable to go yourself, you could employ a researcher. Researchers in the PRONI area: http://sgni.net
You haven’t said what denomination your ancestors but the era (1700s) plus the journey Antrim – North Carolina, combined with a Scottish surname all strongly suggest they were Presbyterian. So Scottish origins are likely. Presbyterianism was established in Scotland in the mid 1500s and brought to Ireland in the 1600s by Scots settlers. Something like 200,000 Scots settled in Ireland in the 1600s, representing 20% of the entire Scottish population. Most settled in the counties of Ulster. Many weren’t very content in Ireland and, having already moved once, were prepared to move again. Many moved to the Carolinas, often encouraged by their Ministers who sometimes went with them. In North America today they are generally known as Scotch-Irish and here in Ireland we call them Ulster-Scots. Most of the folk who left Ireland in the 1700s were Presbyterian Ulster-Scots. Native Irish (if there is such a term) didn’t start emigrating in large numbers till the 1800s.
You will probably struggle to trace your ancestors in Ireland due to the general lack of records, especially if you have no idea of where in Antrim they may have lived. Only about 6 Presbyterian churches in the county have any records for the 1700s though there were dozens of congregations at the time. Most weren’t keeping records or if they did, they later lost them. Nearly all the surviving records are in PRONI. Cullybackey Presbyterian has records from 1729 when it was established. Those records are in the Presbyterian Historical Society in Belfast.
Production of lace is quite possible. Most families in Ulster at that time did a bit of weaving. Mostly produced at home on hand loom weaving machines such as are still used in the Outer Hebrides to make Harris Tweed. The looms were collapsible for convenience if they were not needed or if the family were moving. They could work with most materials eg cotton, linen, lace (damask), calico etc. What they produced varied over the years. Up until the American War of Independence they had worked with cotton (imported from the Carolinas) but the naval blockade during the war cut off supply, and so they switched to linen instead. (Linen comes from flax which grows well in Ireland in contrast to cotton which doesn’t grow here at all).
I wouldn’t take too much notice of the spelling of your family’s name (ie the extra e). Most folk in the 1700s were unconcerned about spelling and it varies all the time according to the whim of the person recording the information. (The playwright William Shakespeare was a highly educated man but the spelling varies in all the 10 or 11 surviving examples of his signature). In 1899, the Rev Smith reviewed the early records of Antrim 1stPresbyterian church (covering the years 1674 to c 1736). He noted: “Even the same word is not always spelled alike by the same hand. Indeed spelling with most of the recording officials (and they must have been fairly numerous) was a matter of the most sublime indifference. The name William, for instance, is spelled 3 different ways in as many lines; while Donegore, a neighbouring parish, is spelled 10 different ways; but these extend over a good number of years. Many families names are spelled phonetically, while others are given in the most round-about fashion.”
So expect spelling to vary. That was the norm.
I looked at the 1901 census of Co Antrim and there were 58 Forsyth and 412 Forsythe. Same census in Scotland there were 5560 Forsyth and 98 Forsythe. So yes Forsyth is more common than Forsythe in Scotland but that was in 1901 when folk were a bit more literate and when officialdom was starting to bother a bit more about accuracy (though not that much). Back in the 1700s nobody bothered at all.
