Terry,
Not sure if you are familiar with the Ordnance Survey memoirs. They were compiled in the 1830s and describe each parish in some detail. There is a name index, so I can tell you that your Shannon grave is mentioned there, along with Shannor & McShannor which are both surely the same name. I have attached the page that mentions your family graves. The description was written in 1839 and it’s always interesting to read what was legible then.
The whole area around Ballynure was heavily settled by Scots who introduced Presbyterianism to Ireland. They arrived 1606 onwards. That Ballynure area was swamped by them. The OS memoirs comment that the local Presbyterian church had over 500 in the congregation compared with 20 - 30 Church of Ireland and 150 Methodists. So few RC they didn’t have a dedicated priest. So in my opinion, your ancestors were probably Scots. That being so, Jamie MacShannon and wife Jean are probably close to first arrivals. You are unlikely to get any further back with your Irish research, even if we had any records for you to research, because your ancestors probably lived in Scotland before that generation. They may have arrived with the Hamilton & Montgomery settlements around 1610. Many of those came from Ayrshire.
https://discoverulsterscots.com/history-culture/hamilton-montgomery
You are interested in ancestors in the 1600s and 1700s. These are extremely hard periods to research due to the lack of records. Much Irish research comes to a stop around 1800 because of the problem. We call it the 1800 barrier. You don’t often break through it unless very wealthy or notorious in some way, or a Quaker. (They kept splendid records that go back to the 1680s).
Ballynure Presbyterian church only has records from 1819 onwards. It opened in 1748 but either no records were kept till 1818 or they have been lost. Before 1748 the congregation around Ballynure attended Raloo Presbyterian church which opened in the 1670s. Prior to that Presbyterians used barns or for a short period Church of Ireland churches after the Church of Ireland service was complete. And some early Presbyterian services were in the open air due to the lack of a church (or Meeting House as it often called). So no record keeping then.
I had a look at the British Newspaper Archives site for Shannon/M’Shannon and Ballynure 1700 - 1850 but without success. No drunkenness, straying cattle or boundary disputes to report. Shannon is a tricky name as it produces thousands of references to the river, and M’ (the original way of writing Mc & Mac) likewise produces thousands of false matches.
If your ancestors had a gravestone in the mid 1700s, they were exceptional. Most couldn’t afford one then. They must have been farmers or otherwise successful financially.
I searched the tithes for Shannons farming in the Ballynure area in the 1830s. the only one I could see was John who farmed in Grange of Doagh in 1834. So possibly yours had all died out or emigrated.
This was the only Shannon family I could find in the Ballynure area in the 1901 census. They were Presbyterian.
http://www.census.nationalarchives.ie/pages/1901/Antrim/Ballynure/Legaloy/991048/
Possibly DNA testing may be a way of matching with others who have additional information about where the family originate. Family Tree DNA reportedly has more people with Ulster roots than any other company. That obviously increases the chances of finding a match. You might want to try them or, if you have already tested, you can transfer your results to them for no fee.
The North of Ireland Family History Society is running an Ulster DNA project and can offer FTDNA testing kits at a reduced price. http://www.nifhs.org (Go to DNA project on the website).