Wife's or mother's surname mis-transcribed?

Priests usually gave the mother's maiden surname in baptismal records, but I've seen cases where they used the married surname instead, often by lisitng the parents as, for example, "John and Mary Ryan".  The birth order you found does make it look as though that might have happened.

However, there's a decent possibility that the Mary Ryan you found is a different person from that Mary Cunningham.  According to MacLysaght's Surnames of Ireland, the Ryan surname was found in two places originally in Ireland, but the largest "clan" by far was in Tipperary, and the surname is so numerous there that it's the most common name in the county, with there being something like four times as many Ryan's as those of any other surname.  When an area has a large number of people with the same surname, it's not out of the ordinary to find spouses who had the same surname, who of course may be related distantly.

Baptismal records frequently state the townland in which the family lived, so one thing to check is whether the Ryan-Ryan birth occurred in the same townland as the other births.  Even then,. though, some townlands back then had very large populations, and it could be a case of third or fourth cousins from the same townland marrying one another.  I have a couple cases of that among my own ancestors (in Mayo).

Thanks for your reply - so difficult to nail anything down with certainty where Irish records are concerned. I seem to recall that those records were rather sparse but I will re-check whether any more detailed locations were given. I was drawn to this family by a connection with a possible dna match, so maybe I'll let that tip the balance. You are certainly right about the proliferation of Ryans. But descended from Powers in Waterford I'm used to that!