Thankyou, Falkryn, for your posting. This site is indeed where I found the reference to Tullyneuh, but have still not been able to find any reference to a Tullyneuh in any county in Northern Ireland. Where did you find a reference to County Derry? The only one I could find by googling was a query from someone also researching McCaughey's in Australia. Unfortunately her email address is no longer current.
I wondered if there may have been a mistranscription of Tullyneagh, like the Lough, but that is in County Armagh. I have read elsewhere that Sir Samuel was bron near Ballymena and this fits with family lore.
I am awaiting an interlibrary loan which may help.
Thanks again for your posting.
Megan