Birth registration started in Ireland in 1864. Marriage registration for non RC marriages started in 1845. Prior to that you need to rely on church records. To do that you need to know what denomination the person was. In addition not all churches have records for the period you need, and where they do exist they are often not on-line.
I looked in the 1901 census for Armagh. There was just 1 Breadner household in the county. They lived in Killyreavy in the parish of Derrynoose, and were Presbyterian (so probably Scottish origins).
None in Keady. But the 2 parishes are adjacent so it’s something to bear in mind as possible relations. Parish map on this link:
If your family were Church of Ireland, then Keady has records from 1780 onwards with gaps. There was also a church in Armaghbreague but it’s early records were lost in the 1922 fire in Dublin. If Methodist, then Keady has baptisms starting in 1815. The records are now kept in Armagh Methodist church. Methodists then were still marrying in the Church of Ireland so they don't have any marriage records for the period you are interested in.
Armaghbreague Presbyterian has baptisms from 1908 and marriages from 1848. 2nd Keady Presbyterian has baptisms & marriages from 1819 (with gaps). The records are still held by the church. Tassagh Presbyterian has records from 1843. 1st Keady Presbyterian has baptisms from 1838 and marriages from 1845. Derrynoose Church of Ireland has records from 1710 (with gaps).
Except where the records are in the Ministers custody, copies of the others are held in PRONI in Belfast. A personal visit is required to view them. If you are unable to go yourself, you could employ a researcher. Researchers in the PRONI area: http://sgni.net
This is the abstract (summary) for the only Breadner will in the county in PRONI’s records, post 1858:
Breadner James of Killyreavy county Armagh farmer died 3 January 1928 Probate Belfast 26 January to Hannah Breadner spinster. Effects £52. (The will itself is in PRONI in paper format).
There was a Robert Breadner who died around 1804 and whose probate was granted on 18.4.1804. The file itself was lost in the 1922 fire. All we know now is that he lived in Tassagh, parish of Keady, and probate was granted in 1804. There are 3 Breadners in Drumhirk (parish of Derrynoose) in the pre 1858 records. Elizabeth died 1829, another Elizabeth in 1831 and a John of Liverpool (late of Drumhirk) who died in 1833. Again the files themselves were destroyed in 1922. The 2 Elizabeths would have been either spinsters or widows. (Married woman didn’t leave will then).
Your best bet is probably to go through the church records I have mentioned to see if you can find the family there. They are not in the tithe applotment records for Keady (which lists farmers), so were presumably labourers/weavers/servants or following a trade that did not involve having land. Always a bit difficult to trace as they often tended to move around to follow the available work.