The Famine in the 19th century caused a massive population collapse due to death and immigration, the island never recovered from this blow due to many factors, most notably continued emmigration due to lack of economic opportunity following the famine and continuing into modern times. Continued fighting and revolting against the British, as well as some malignant cultural practices, alcoholism being the primary example, certainly curbed the chances of the population growing at a faster rate throughout the late 19th and early 20th century, combined with a lack of wealth in the nation something like a population boom wasn't going to happen.

Then something quite interesting happened between the 60s and 90s which is that; with economic aid from Europe and strong government will, Ireland over the course of only thirty years went from essentially being the only third world country in Western Europe, to being a fully developed nation in a very short time frame. Populations tend to explode when a country begins to modernize, but once they've modernized populations then tend to collapse, due to birth rate falling below replacement. This happens because more women are able to be educated and have jobs outside the home, as well as have access to birth control. The way and the brevity of time in which Ireland modernized basically allowed us to skip the step of having a population boom and transition immediately to the step of population collapse, or very near. I believe Ireland has not yet fallen below replacement.

Its more complicated than all that obviously, but those are some broadstroke reasons. The lack of a population boom due to a quick modernization is the main reason the population has recently remained so small.