To invade Ireland, the Romans would first have needed to gain full control of either Wales or the Clyde estuary in Scotland, something they never succeeded in doing.
The Romans very much wanted to conquer Ireland, because the Irish were a constant source of weapons and "rebellibus" support to the Scots and Welsh for attacks on Roman communities. During the fifth campaign of Agricola he reached partem Britanniae quae Hiberniam aspicit (the part of Britain that faces Ireland), but he never controlled it sufficiently to attempt a crossing.
During his invasion of Scotland, Agricola had to build a large number of forts, which has been great for archaeology, but not so great for the Romans, since it became very expensive to fend off the Gaels. This was the same in Wales, where a string of costly forts had to be maintained to protect against Irish-sponsored attacks. The graphic below, showing Roman and Gaelic forts, illustrates the line of control:
The green and violet is Roman; red, blue, yellow and orange Gaelighe. Although the large number of green dots suggest Rome might have controlled most of Wales, this is not the case. The solid line of control were the "castles" (the violet dots on the right), which were Chester, Wroxeter, Lanchester (mispelled as "Kanchester" in the map) and Gloucester. The other forts were in "allied" territory, which was semi-autonomous and not under full control (hence the need for lots of forts). The orange line of "Offa's Dyke" (a structure of uncertain history, shown on the map) shows where Roman authority more or less ended.
The Gaels were very keen to control the area because there are a lot of tin mines there, which is needed to make bronze, their main weapon material.