Karen,
If Andrew Givens came from Carnteel and was Presbyterian, then the 2 nearest churches he may have attended were Aughnacloy and Ballyreagh. Unfortunately Aughnacloy's baptism & marriage records don?t start till 1812, and Ballyreagh?s in 1843. So you are unlikely to find his birth (or marriage if he happened to marry there too).
I note that son William was born in Tyrone in 1821. It might be worth checking the Aughnacloy records for that baptism. The records are not on-line anywhere, so far as I am aware, but there is a copy on microfilm in PRONI, Belfast.
The surname Arneil is not common in Ireland. Looking at the 1901 census there were just two households throughout the whole of Ireland. Both in Belfast, one was Presbyterian, the other Church of Ireland. (Tradition was to marry in the bride?s church so you need to consider the poissibility she wasn't Presbyterian).
No trace of the marriage on the usual Irish genealogy sites, but not all church records from that period have survived.
Griffiths Valuation for 1860 lists only 3 Arneil households throughout Ireland. Two were in the same townland (Drumfad) in Co Tyrone, not too far from Carnteel, so that?s a hint that Margaret may have originated there. Drumfad is in the parish of Killeeshil. One farm in Drumfad was rented by Thomas Arneil and immediately bedise it was another tenanted by Martha Arneil (probably a widow). The modern Goland Rd runs through Drumfad, near the Ballygawley roundabout.
I would normally recommend checking the local church records for that parish in case that?s where Margaret came from and so where they married. Unfortunately the Church of Ireland records prior to 1881 have been destroyed (in the 1922 fire in Dublin). The local Presbyterian records for Clonaneese Lower start in 1811 for baptisms but only 1845 for marriages. Clonaneese Upper has nothing prior to the 1860s. Therefore there don?t appear to be many relevant church records available for the period you are interested in. Presbyterians don?t keep burial records either, so that won?t help.
I note that Andrew was described as a flax weaver. That indicates that his family were pretty poor and would likely have had a small cottage on someone's farm (generally paying their rent by an agreed number of days work a year on the farm). Weavers often don?t make it into official records very much, living below officialdom?s radar for much of the time, and so it?ll be very had to find anything on the family.
One check you might want to make is with the GRO in Southport, England, both for the marriage and for any childrens births (at least whilst Andrew was still a serving soldier). They have details of marriages and births & death of British military personnel, starting in 1761. Here?s a description:
"Regimental Birth Indexes ? may show several index references for the same person. As a soldier moved from one regiment to another, he had to register himself and his family each time for pay purposes. If you find more than one index reference for same person, provide all references and we will produce the entry with the most information. There is no index for Regimental Marriages or Deaths. However, for Regimental Marriages, if a regiment and a year can be supplied, a search can be undertaken. If Royal Artillery, then a battalion or battery will be needed."
https://www.gro.gov.uk/gro/content/certificates/Login.asp
The military pension that you enquire about would have been paid in sterling. It was probably ?6 a year. (A labourer?s income at that time was about ?20 a year).
Elwyn