The Society of Friends? records for Armagh are listed but
not till 1864 and civil registration according to the
History Foundation. I do know that all faiths were baptised in the Church of Ireland to a certain point in history. Even RC
if there was no church in the area, often burials in church yards had multiple religions.
I think there are Quaker records for Ireland but can't remember where I came across them.
You could try www.cyndislist.com
who might have those resources listed. If not google. There are separate Jewish records as well not listed with the Foundation.
There are other websites but most are competition with ancestry/rootsweb.