His parents might have married before records began in 1806 or they may have married in a different parish. (Tradition was to marry in the bride’s church so if she came from another parish nearby, they may have married there. But again records may not exist. Very few rural parishes in Ireland have records before the 1820s. If it is of any consolation, if you did find a marriage, a record from that era would not contain much information. Often just the date, the couples names and their 2 witnesses. No parents names or townlands, or anything like that.