There are some tantalising hints about a Roman presence in Ireland, at least in the 1st/2nd centuries AD (or CE if you prefer).
Some verge on the conspiracy theory - notably the suppression of genuine finds because they contradict the "official" view that Erin was unconquered. Much of these centre around the (alleged) finds at Drumanagh, a Roman Fort, Trading Post, Complete fabrication...take your ideological pick. From what I have seen the debates tended away from the polite exchanges of academia and descended into vituperative name calling - no difference there from normal behaviour then.
Others come from Irish mythology - Tuathal Teachtmar, the 106th High King won his position after returning from exile in Alba (Britain). He existed sometime between 50AD and 150AD (probably High King from 80 - 106AD). He has been tentatively identified as being a prince of Ireland mentioned by Tacitus in Agricola. Some Roman support is, therefore, possible. Juvenal also hints that Roman arms went to Ireland.
I have read, although I can't quite remember the source, of a multi-limbed and fanged monster that devoured armies - the source suggested that it could describe a legionary / auxila cohort in close order drill chewing through native levies and thus a description of a real roman armed force on the island. This may be a touch too fanciful.
My own opinion, is that during the apex of Empire, the Romans exerted some level of trans border influence in Ireland, client kings etc, as they did in other parts of the Empire. However, as this was normal behaviour and not directly run by the emperor, it would be downplayed by the central authorities. Cetainly there was trade and Ptolemy does give a reasonably good description of Ireland and its tribes.
As an aside, and often mentioned in discussions about Rome and Ireland, there is little archeological evidence for Caesar's invasion of Britain. But, so far as I am aware, no-one disputes that it happened, mostly as a result of Caesar's Commentaries (which, I hasten to add, are not the most objective of sources) supplemented by other contemporary writings.