I will start by saying I am not a geologist so hopefully someone has a better answer. Initially, your sample does look like massive epidote, but the local geology doesn't support that identification well.
Using the geological map found here, Geological Survey Ireland Spatial Resources, there are a few distinct types of bedrock geology in the Barnesmore Gap, two are ancient granites, two are a conglomerate type rock with pale green chloritic matrix, there are also shale, limestone, marble containing areas west of Barnesmore. The interesting thing to note is that the area, particularly associated with the granite zones, has a number of dolerite dykes, intrusives of mafic magmas, these bring with them the possibilities of pyroxenes, with diopside and jadeite having the right hardness, specific gravity, and perhaps lustre. So the green material could be from the dykes in the form of pyroxene or if the lava was more mafic even olivine.
Alternatively, epidote is often associated with hydrothermal events and marble, there doesn't seem to be any dykes in the marble containing areas but that doesn't mean there couldn't be some hydrothermal alteration due to the recent dykes in the area. So massive epidote is a possibility, but overall there doesn't seem to be much in the way of other hydrothermal alteration in the area so this option is not 100% either.
Overall the rock looks like like it contains epidote but it could also be a number of other minerals. I would suggest flaking a small crystal of the green mineral off so that cleavage and transparency can be assessed.