Birth and death registration didn’t start in Ireland till 1864, non RC marriages 1845, RC marriages 1864. So your family married and were having children long before those dates. You might be able to find their baptisms and marriage if the records still exist. However those records may well not be on-line.
First thing we need to know was the family denomination. If Church of Ireland (ie Anglican) and Portadown is accurate, you could search the records for Drumcree which start in 1784, and Portadown itself whose records start in 1826 which is possibly when the church opened. If they were of another denomination, let me know and I’ll tell you what records are available. However looking at the 1901 census for Armagh there were 30 folk named Rowe. All were Church of Ireland, so I’d start with it.
The Drumcree and Portadown records are held in PRONI in Belfast. Personal visit required to view them. I don’t think either set is on-line anywhere yet.
Bear in mind that tradition was to marry in the bride’s church after which she’d attend her husband, so the marriage might not be in the same church as the baptisms.
If Portadown is not correct, then you could widen your search to adjacent parishes but there’s quite a few.
https://ulsterhistoricalfoundation.com/getting-started/ulster-civil-parish-maps/county-armagh