To get you started - the Ecclesiastical Directory of Thom's 1868 and 1869 confirm that Right Reverend Nicholas Power was Coadjutor Bishop of the Diocese of Killaloe, the Bishop is listed as Right Reverend Michael Flanney D.D. I've attached a list of the parishes of the Diocese and an image of the listing for 1869. There's a James Ryan P.P. at Youghal-Arra parish but no sign of a Patrick Ryan among the Parish Priests or Curates officially assigned to any of these parishes. Possibly he didn't serve here long enough to be listed.
The Ryan surname is the most common surname in Co. Tipperary so multiple household with similar name, making searches difficult. The baptism registers for the parish of Nenagh go back to 1792, but there is an unfortunate gap in the surviving records between December 1842 and January 1845 - possibly lost or damaged pages (the last few pages for 1842 some some damage & missing sections). The register images for the parish are available on the National Library of Ireland website - see Nenagh RC parish.
To allow for the 'near Nenagh' reference it might be worth checking the adjacent parishes :
I'd allow a little leeway with regard to the date of birth - people rarely knew their exact date, in any case early baptism records do not usually include this detail, just date of baptism. However at that time Catholic baptisms usually took place within a couple of days of the birth (sometimes the same day. It might be worth checking for full civil death record for Patrick in case his parents are named, as this could help locate his family e.g. by searching for younger siblings, also might be worth tracking marriage and death certs for Michael to see if any family details are mentioned.