I recently received information from the Tipperary Heritage Center regarding John Teefy and his father Patrick. In searching for my ancestors, they came up with two possible matches. They're posted below for anyone who might be researcing either family.
John Teefy - born/christened 19 August 1817.
Parish: Newport
Address: Cully
Father: Patrick Teefy
Mother: Mary Kinnelly
Sponsors: Hugh Teefy and Mary Conry
Register #: Newport/1324
The second match was:
John Teefy - born/christened July 3, 1819
Parish: Newport
Address: Unknown
Father: Patrick Teefy
Mother: Biddy Skeahan
Sponsors: Michael Hourigan and Catherine Teefy
Register #: Newport/1325