Hi Terry,
Hopefully you will have some success.
[Modulo the usual ravages of time/weather/GPS/ etc. ...]
SHANNON, SHANNOR & McSHANNOR are all reported as "families who bury and have vaults, tombs and headstones in Ballynure churchyard".
The oldest headstone is dated 1714.
[Ref: Ordnance Survey, Memoirs of Ireland, Ballynure and District, 1832~1840, Vol. 32, page 56]
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Within Ireland the SHANNON name is most numerous in Co. Antrim.
It has multiple possible derivations.
In the Glens of Antrim, it derives from "Mac an tSionnaigh" - "son of the fox".
[Folks of a Protestant persuasion tended to anglicise this as SHANNON.
Folks of a Catholic persuasion tended towards FOX or TODD.]
The name was also common in Scotland, particularly in Galloway & Kintyre.
A sept there were harpers to the MacDONALDs of Kintyre.
This area was the Britain-ish outpost of the Antrim based Dalriadian "empire".
There the Irish originated O SEANAIN name was often rendered MacSHANNON.
[In the 16thC & early 17thC the area was a major contributor of "Scottish" settlers in Ulster.]
Ref: The Book of Ulster Surnames, Robert Bell, The Blackstaff Press, ISBN 0-85640-405-5 pp. 228-229
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If you are visiting from abroad I'd suggest that it would be well worthwhile trying to engage some of those marvellous folks from the Ballyclare Historical Society for an afternoon, some of whom do historically-informed tours of Ballynure.
[But you'll have to be quite persuasive ... they can be very shy/modest/busy ...
Ref:
http://www.ollar.utvinternet.com/ ]
Capt. Jock