Reywd:
I searched the subscription site Roots Ireland and located a baptismal record for a Richard Dwyer on October 16 1816 at the Pallasgreen/Templebredon RC church in Co. Limerick. Father was William Ryan and mother Bridget Humphries.
I also located a March 27 1822 baptismal record for a Johanna Ryan in Pallasgreen/Templebredon Father was Richard Ryan and mother Catherine Ryan.
Note the dates are baptismal dates and the children were likely born a few days before the baptismal date. Also, there were so many Ryans in the parish that Ryan was likely the maiden name for Catherine Ryan not her married name.
The only marriage record I could find for a Richard Dwyer to a Ryan was a February 21 1843 marriage between a Richard Dwyer to an Anne Ryan at the Oola/Solohead RC parish in Co. Limerick which is the parish just to the east of Pallasgreen very close to the border with Co. Tipperary. Possibly Johanna went by Anne when she was married but it is also possible that this is a marriage record for an unrelated couple.
Also you mention " I knew he was from Co. Tipperary" . Can you clarify?
You may want to consider a DNA test to identify possible 3rd and 4th cousins.
Roger McDonnell