The surname Graham is very common in Ireland. In the 1901 census there were 8494. 303 were named Thomas, 20 of those in Fermanagh and 20 in Monaghan. It would have been equally common in 1801. Tracing your Thomas without some specific idea of where he originated and what his parents names were is a needle in a haystack.
To complicate matters further, for a birth around 1801 you need to rely on church records, but many churches don’t have any for the that period. It would also be helpful to know his denomination, as that can help to narrow the search a little.
Traditionally, many Grahams in Ireland are descended from settlers who arrived in the 1600s from the Scottish Borders. Many of those settled in Counties Fermanagh and Monaghan.