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 1816 before Methodists agreed to conduct their own baptisms. However because of continuing loyalty and other factors, many continued to use the Church of Ireland for sacraments for many years after this date and it was 1871 before all Methodists routinely performed their own baptisms.
For marriages, the earliest ceremonies conducted by a Methodist Minister in Ireland that I am aware of, date from 1835 (Belfast Donegall Square). However in the mid 1800s there were only a few Methodist Ministers in Ireland (Methodism relied heavily on lay preachers). So the shortage of Ministers contributed to the continuing practice of marrying in the Church of Ireland.
So to summarise, you are unlikely to find any Methodist baptisms much before 1830. Few marriages before the 1840s and only a few for many years after that. If there are no Methodist records in the location you are interested in, I would search the Church of Ireland instead, as that’s the most likely place to find the relevant event.
Few Methodist Meeting Houses have graveyards and so most are buried in public or Church of Ireland graveyards (which are open to all denominations).
Edgehill Theological College in Belfast has a historian who should be able to advise you of any Methodist records in the Longford area, and where they are held.
http://www.edgehillcollege.org
