Birth, death and RC marriage registration didn’t start in Ireland till 1864 (in contrast to England where it was 1837). Prior to 1864 you need to rely on church records.
I assume that John & Maria were Catholic, and that they married in Ireland. I searched the on-line parish records on Ancestry for a marriage and for any children to the couple, in Armagh but without success. Possibly they came from a parish with no records for the 1840s or earlier.
If they moved to England it’s always worth checking the English censuses in case they put a specific place of birth. Usually it was just Ireland but sometimes you get more. Likewise obituaries and will occasionally throw up some information.
Otherwise I am sorry but I cannot provide any additional information on the family.