Hi there,
I have had a look and whilst I'm sure they will be related I don't have them in my records.
Whereabouts is Burren Rig? and whaat info do you have on James born in the 1790's?
I have a James Thornburn born 1775 who is a brother to Walter my xtimes grandfather.
I have a James as living in St Annes, Johnstone in the 1841 census with his wife Elizabeth aged 65 and 55.
I have a list of their children and in both 1803 and 1807 they had a daughter baptized as Betty, which is, of course, Elizabeth. I never got the originals so I don't know if the place of birth was recorded.
My Walter also married an Elizabeth but I don't know if they had a daughter named Elizabeth, quite likely, I would have thought.
The 2 residences I have are Elizatown and Kinnelknock.
Hope this helps...
cheers
Norma