Searching for information on the Pennington's

Statutory birth, death and marriage registration (in some jurisdictions called Vital Records) only started in Ireland in 1864, save for non RC marriages which were recorded from 1845 onwards. So you probably won’t find statutory birth, death or marriage certificates in Ireland for this family. For earlier years you usually need to rely on church records, where they exist. You obviously need to know the precise denomination in order to search the correct records. Not all churches have records for that period and not all are on-line.

RC records are mostly on-line on the nli site:  

https://www.nli.ie/en/family-history-introduction.aspx

For other denominations, the churches usually hold the originals but there are also copies in PRONI, the public record office, in Belfast. A personal visit is required to access them. Access to the records there is free. This link explains what records exist, parish by parish:

https://www.nidirect.gov.uk/publications/proni-guide-church-records

If you are unable to go yourself, you could employ a researcher. Researchers in the PRONI area: http://sgni.net

Looking at Griffiths Valuation of Ireland (1863) there are only 3 Pennington households listed in Co. Armagh. All 3 are in the parish of Ballymore. One (Henry) was in the townland of Lisnakea, the other two (William & Charles) were in the townland of Ballymore.

Looking at the 1901 census of Co. Armagh there were 14 Penningtons in the county. 13 were Churhc of Ireland and 1 was Presbyterian. There was a Henry Pennington in Lisnakea:

http://www.census.nationalarchives.ie/pages/1901/Armagh/Tandragee_Rural/Lisnakea/1021076/

It’s obviously not your Henry but families often repeated names generation after generation, so there’s a chance this family is related.

So I would focus on Ballymore Church of Ireland records to see if your family are in them. There are 3 Church of Ireland churches in the parish. The early records for those at Acton and Clare were both destroyed in the 1922 fire in Dublin and they have nothing before 1877. However the main church at Ballymore does have records from 1783 onwards.  This is what PRONI has, according to their catalogue:

Baptisms, 1783-1923, which include a list of Presbyterians baptised, 1822-31; marriages, 1783-1908; burials, 1783-1899; vestry minutes, 1771-1810;

vestry account book, 1821-7; confirmations, 1843, 1846, 1849, 1852 and 1856; estate rental for the manors of Ballymore, Acton, Clare etc., possibly used for tithe or cess purposes, 1812-27; history of the church from the 17th century.

Some probate abstracts from the PRONI wills site:

The Will of Henry Pennington late of Lisnakee County Armagh Farmer who died 9 February 1887 at same place was proved at Armagh by Jane Pennington of Lisnakee Widow and Alexander M'Cullough of Mullintur in said County Farmer the Executors.

Pennington Henry of Lisnaskea Tandragee county Armagh farmer died 12 March 1936 Administration (with Will) Belfast 20 October to Samuel James Pennington farmer. Effects £1070 15s.

Pennington, Samuel James of Lisnaskea Tandragee county Armagh farmer died 14 February 1963 Administration Belfast 17 September to Maude Pennington the widow. Effects £8873 9s.

There were two farms in Lisnakea listed in the tithes in 1830, held by Edward & Henry Penton (Penton being a variation of Pennington).

http://www.irishgenealogyhub.com/armagh/tithe-applotments/ballymore-parish.php

I can’t say that the Lisnakea farms are definitely your family but it seems the obvious area to start. The family is likely to be descended from English settlers who came to the area in the 1600s, probably as part of the Plantation.

Thank you Elwyn You have been Very Helpfull, I believe they were Presbyterian, I will look into all suggestions, Thank you again. Steve