Linda,
Research in Ireland in the 1700s is always very difficult, mainly due to the lack of records. The area around Connor is no exception. Connor Presbyterian church has no records before 1819. There is also a Presbyterian church nearby in Kells but it only opened in the 1860s and so could not have been the one your family attended.
If your ancestor married in Connor in the late 1600s and had children baptised there around 1700, there are no church records to search (of any denomination). I cannot think of any way of obtaining local information about him. You mention that one of the children was called Macdale or Macdole. Madole (sometimes spelled McDowell but pronounced Madole) is a common enough name in Ulster, so it might be that.
There was no requirement to produce passenger lists in the 1700s, and very few exist. Where passenger records do exist they tend to be in North America, rather than in Ireland.
I can recommend Dr Wm Roulston’s book “Researching Scots-Irish ancestors – The Essential Genealogical Guide to Early Modern Ulster 1600-1800” if you want to study what is available. In general, the records referred to there are not on-line and involve going to PRONI in Belfast or the National Archives in Dublin.
It’s probably worth commenting that your ancestors may not have lived in the Connor area very long. The main migration of Scots to Ireland was in the 1600s. Some came with the Plantation and the Hamilton & Montgomery settlement in the early 1600s, others came throughout the 1600s for a variety of reasons and there was a big surge in the 1690s due to famine in Scotland. Something like 200,000 Scots settled in Ireland in the 1600s (around 20% of the entire Scottish population). Many settled in Antrim. If they were Presbyterian, with a Scottish name like Adams, and were living in Co. Antrim then there’s not much doubt your ancestors originate in Scotland. They may only have lived in Ireland for as little as 20 years before moving again to North America. The first big migration to North America was in 1718. Background here:
https://www.ancestryireland.com/wp-content/uploads/2017/08/The_1718_Migration.pdf
Connor is pretty small. Not much more than one street really. You may find some tourist information on the area on this tourist board site
https://visitbelfast.com
