I recall in my sedimentology course one exam where we were given buckets of sand. We had to identify the approximate location of the sources of each sample within a few miles. I don't remember the specific distance, but it was surprisingly small and the sand samples came from basically anywhere in the U.S.

At the beginning of the course we all understood that by the end we would be asked to do this and it was intimidating. But by the end of the course and in practice, we were all pretty able to make the location identifications accurately. This was just an undergraduate course in sedimentology and composition of the sand grains where easy enough to separate identify the composition of and at what percentages. If I recall correctly.

Other types of rocks, igneous and metamorphic would use different methodologies for identification. Now you picked that rock up from a beach in Ireland. It's just one rock, how did it get there by what action? Waves, maybe a glacier or two, rivers? Because Ireland is an island I'd greatly suspect that it's from Ireland but with glaciation it's conceivable that it's path to that beach started out at a granite or metamorphic rock formation further north from where you found it. Heck when you involve the actions of glaciers, your rock could have started out in Scotland, but probably not. It could be a simple black basalt from the ocean bottom. That would be difficult to identify, but even those have different properties that a lab with the right comparative samples could identify.

Since you found your keep sake on a beach it still could have formed anywhere and was transported there by many actions over millions if not billions of years. It could have been a gastrolith in the belly of a dinosaur that migrated across the continent when there were land bridges. I just googled to see if there ever any dinosaur remains found in Ireland and was somewhat surprised to find that there are a few. But the odds of your rock being a gastrolith from the belly of an Irish dinosaur is about the same as both you and I winning the jack pot in the lottery.

Rocks are awesome things, and it's possible to differentiate your rock from any that might be found here. But when we are just dust millions of years from now, someone/something could pickup your rock again and ask a similar question about it. So now it's an American rock that currently holds your memory of Ireland. I love Ireland.