Jorina,
Methodism took a lot longer to become established in Ireland as a separate denomination than in England. In Ireland there was considerable resistance to separating from the Church of Ireland. It was 1815 before Methodists started to conduct their own baptisms. However because of continuing loyalty and other factors, many continued to use the Church of Ireland for baptisms and marriages for years after this and it was 1871 before all Methodists routinely performed their own baptisms.
For Methodist marriages, the earliest that I am aware of, date from 1835 (Belfast Donegall Square, the first Methodist church in Ireland). However in the mid 1800s there were only a few Methodist Ministers (Methodism relied heavily on lay preachers). So the shortage contributed to the continuing practice of marrying in the Church of Ireland. In addition, in the early years, many Methodist Meeting Houses were not licensed for marriages so that too contributed to couples marrying in the Church of Ireland.
So to summarise, you are unlikely to find many Methodist baptisms before 1820. Few marriages before the 1840s and only a handful for many years after that. If there are no Methodist records in the location you are researching, I would search Church of Ireland records instead, as that’s the most likely place to find the relevant event.
Not many Methodist Meeting Houses have graveyards and so they may be buried in public or Church of Ireland graveyards (which are open to all denominations).