I search the IFHF's online database @ ROOTSIRELAND.IE. It has abt 19 million B/M/D and other records for MOST Irish counties. Records before 1863 are increasingly sparse. Many B/M/D events weren't recorded, or the records haven't survived.
For W(illiam) Robinson B 1860 (exact), somewhere in Ireland with the parents' names unknown, I found 4 records: none are in Co. Tipperary. Note - the RC church refused to contribute its records for transcription by the IFHF. These are available through the Tipperary Family History Research Center (at a substantial fee).