Birth and death registration didn’t start in Ireland till 1864. Non RC marriages weren’t recorded before 1845 and RC only started in 1864. So you won’t find birth certificates for someone born c 1821, nor a marriage cert for a marriage before April 1845. You might find baptism and church marriage records but not every church has records for that period, and of those that do, not all are on-line.
I don’t see a marriage for Nathaniel Smyth & Matilda McCaughan 1845 onwards. So may have married pre 1845, in which case you’d need to search local church records. But were they actually married? I found a marriage for Nathaniel Smyth of Teeshan in 1847 who was a bachelor (aged 35) to Peggy McIlroy. Perhaps he never married Matilda and his marriage to Peggy might be the reason she left for Australia, still a single woman?
Griffiths Valuation has a Nathaniel Smyth farming plot 14 in Teeshan in 1862.