Cindy,
None of the church records held at PRONI are on-line. Their catalogue is on-line so you can see what churches they have and what years, but the records themselves are not on-line. They are on microfilm or, in some cases, paper format, and you need to go and browse them yourself (or employ a researcher).
This is what PRONI has for Ballymena Presbyterian Churches:
P. 1st Ballymena Baptisms, 1812-1938; marriages, 1812-1906; session minutes, 1812-1925, with gaps.
P. 2nd Ballymena (High Kirk) Baptisms, 1813-1941; marriages, 1845-1936.
P. Wellington Street, Ballymena Baptisms, 1863-1962; marriages, 1864-1920; minute books, 1862-93.
P. West Church, Ballymena Baptisms, 1829-1945; marriages, 1830-32 and 1845- 1903.
N.S.P. Ballymena or Kirkinriola Marriages, 1849-63.
P means Presbyterian and NSP is non subscribing Presbyterian. There is also a Reformed Presbyterian Church (aka Covenanter) but they don?t have any records for the 1800s.
The staff in PRONI will show you where the records are kept, and how to operate a microfilm reader. You then scroll through the films which are copies of the registers, page by page, till you find something you are interested in. You can then either transcribe the entry, or take a photocopy (30p a page).
Carnany Upper is a townland; Dunluce Upper is the barony that it is situated in. Carnany Upper consists of 187 acres of mostly agricultural land. It is just to the east of Ballymoney. The modern Frosses and Landhead Rds both run through it.
The smallest unit of land in Ireland is a townland. (There?s no not necessarily a town in a townland and in the case of Carnany Upper there isn?t. There?s a Carnany Lower too, so you need the Upper to distinguish the two).
Groups of townlands forma parish; groups of parishes form a barony. That?s roughly how it works.
In 1901 there were 9 households in Carnany Upper (no Linns by then).
http://www.census.nationalarchives.ie/pages/1901/Antrim/Enagh/Carnany_Upper/
Griffiths tells me that in 1861 John Lynn had a farmhouse, outbuildings and just under 45 acres (making it a prosperous sized farm for the area). In 1864 the tenant changed to Walter Lynn. (Probably passed from father to son on the father's death). He left in 1895 and James Torrens acquired the farm. (Source is the revaluation records):
http://applications.proni.gov.uk/dcal_proni_val12b/RelatedVolume.aspx?3414
Dorothy Arthur has published several books on graveyards, listing all the inscriptions, in the Ballymoney area. I should think there are copies in Ballymoney library and/or in Ballymena library local studies section. You might find them helpful.
Elwyn