Peggy,
You face the same basic problem as Susan which is that there are almost no church records in Co Antrim for someone born in 1761, and very few other records of their life in Ireland up to 1785 when John Leslie left.
Regarding James being born in Coleraine, not Antrim, it’s worth commenting that Coleraine is very close to Antrim. The county border now is just outside the town. Coleraine is divided by the River Bann. Originally everything in the town west of the Bann was in Co. Londonderry (at that time called Co. Coleraine) and everything east in Co. Antrim. In the early 1600s, for easier administration, it was decided to redraw the boundary so the whole town was in the one county. The county was also renamed at the same time, changing from Co. Coleraine to Co. Londonderry.
So someone born just outside Coleraine could be born in Co Antrim, though they might give Coleraine as their home, especially in the USA where an individual townland in Ireland that no-one would have heard of was probably meaningless.
You ask how the Anderson & Sheriff families connect with the Leslies. They may have all lived close to each other in Ireland. Anderson is a very common name here. There are 2381 of them in the 1901 census of Antrim & Londonderry. Sheriff is not so common though. In the 1901 census there’s just 3 families, and one of them was a shipyard worker from Scotland.
Part of the 1831 census for Co. Londonderry has survived and includes the parish of Coleraine. There were just 2 Leslie households in it (both Presbyterian). One lived in Meeting House Lane in the town:
http://www.census.nationalarchives.ie/pages/1831/Londonderry/Coleraine/Coleraine/Coleraine_Town_Meeting_House_La/133/
The other lived in Winnyhaw (more commonly Windy Hall). Windy Hall is on the southern outskirts of the town of Coleraine. Today it’s a residential area though in 1831 it would have been farmland.
http://www.census.nationalarchives.ie/pages/1831/Londonderry/Coleraine/Coleraine/Winnyhaw/6/
I mentioned Andrew Kane’s book on Coleraine, compiled from records held by the Honourable Irish Society. It mentions several Leslies and a Sherriff. George Leslie is recorded in 1738 as holding 6 acres, 2 roods 37 perches of land (just over 6 and a half acres). The location isn’t given. He appears again under the list of town tenants 1738-58 as leasing a good slate house, two storeys with garrets. He appears to have let that to tenants named James Dodd and later John MacDougal).
Another entry records James Hutchison, Patrick Keith, Isaac Cochrane, John Smith & William Sherriff as tenants or occupants of “An old slate house, two storeys high with garrets.” Samuel Sherriff, Joseph Wilson & Samuel Paterson as holding a property in the town on a 3 lives lease (in this case the King’s first 3 sons) granted on 29.9.1774. (If you want an explanation of that I can do so).
James Leslie is also listed again with a lease granted on 29.9.1774.
The book also details a property on Church St, Coleraine. “Perpetually renewable lease granted to John Smith & Samuel Sheriff and Lord Mark Kerr on 1st July 1774 at £23-5-2pa with associated acre 101. Now held by Joseph Wilson & Samuel Patterson, executors of the will of Lord Mark Kerr, and Mr Sheriff. This trust is currently the subject of a dispute which has delayed the granting of a new lease.”
The late Lord Mark Kerr was the husband of the Countess of Antrim. So his estate was the owner of this land. (At one time the McDonnells, Earls of Antrim, owned a quarter of the county, including most of the land in north Antrim).
Several Andersons and Sheriffs in the tithe applotment records for Coleraine of 1827. The tithes were a tax on land, so these were lists of people with land. Mainly farmers. There are no Leslies so that indicates they didn’t have any land. So the ones in the 1831 census are perhaps tradesmen or labourers, or servants.
One Sheriff in Dundoan in the 1831 census (mistranscribed as Shurff):
http://www.census.nationalarchives.ie/pages/1831/Londonderry/Coleraine/Coleraine/Dundovan/22/
If you are looking for some general background reading on Coleraine in the 1700s, you might find “Coleraine in Georgian Times” by the Rev Mullin (publ 1977) interesting. You get general descriptions of life. For example: “ Arthur Young made a tour of Ireland in 1776. He took a special interest in emigration” Upon going over to Ireland I determined to omit no opportunities of discovering the cause and extent of this emigration. The spirit of emigrating in Ireland appeared to be confined to tow circumstances, the Presbyterian religion, and the linen manufacture. I heard of few emigrants except amongst the manufacturers of that persuasion. The Catholics never went, they seemed not only tied to the country but almost to the parish in which their ancestors lived.”
Or: “ A French émigré, Dr Latocnaye, visited Ireland in 1796 and spent three or four days with Mr Richardson of Somerset, who received him warmly. The Frenchman said that on Sundays the countrywomen of Coleraine resembled those of Scotland near Montrose. They dressed neatly and had a red cloak over their shoulders. Anyone who saw them would not have thought he was in Ireland.”
Most of that part of Ireland was very heavily settled by Scots and so was markedly different to other parts of Ireland. A Presbyterian Minister brought up in Aghadowey, Co Derry (near Coleraine) wrote this of his childhood in the 1820s: “Aghadowey had originally been settled by a Scotch immigration and I found that my new neighbours spoke as pure Scotch as a man might hear in any part of Ayrshire.”[1]
Describing his youth in Ballycahan, parish of Dunboe, again near Coleraine, a local farmer said: “Over a space of 15 to 20 miles from east to west, and about the same from north to south, Scottish surnames, a broad Scottish dialect and an almost universally diffused Presbyterianism indicated the title of the people to call themselves “Scotch”. Episcopalians were few and a Roman Catholic as rare as a black swan.”[2]
[1] Autobiography of Thomas Witherow 1824 – 1890 Page 25. Ballinascreen Historical Society 1990
[2] A Kennedy chronicle – Biography of Alexander Kennedy of Ballycahan 1818 – 1885 by Hugh Alexander Hezlett (Coleraine library)