Well, "overpopulated" is a difficult word to define.
It is certainly true that Ireland had seen a large and rapid population increase in the century preceding the potato famine. The population growth in Ireland was not as great as that in England and Wales over the period, but England and Wales were in the midst of the industrial revolution, and urbanizing more rapidly than Ireland. The population growth in Ireland was about 50% more than that in Scotland over the period.
The population increase in Ireland was presumably enabled by the introduction of the potato as a crop and food source.
In 1740, the population of Ireland was 3.25m.
In 1841, the population of Ireland was 8.2m.
The population of Ireland had grown by almost 5m people, 152%, in 100 years.
http://www.grantonline.com/grant-family-genealogy/Records/population/population-ireland.htm
The population of England was 5.8m in 1750.
The population of England was 15.9m in 1841.
The population of England grew by 174% in 90 years
http://www.visionofbritain.org.uk/census/SRC_P/6/GB1841ABS_1
The population of Scotland was 1.3m in 1755
The population of Scotland was 2.6m in1841.
The population of Scotland grew by 100% in 85 years.
http://en.wikipedia.org/wiki/Demographic_history_of_Scotland#/media/File:ScottishPop1801-2011.jpg
The high population of Ireland in the early 19th century may have been an anomaly. The introduction of the potato as a staple crop had enabled an increase of the Irish population (though most were very poor subsistence potato croppers) which only lasted 100 years before a fungal disease attacked the potatoes, causing the potato famine, and an Irish population decline from which Ireland has still not recovered.
The combined population of the Republic of Ireland and Northern Ireland today is 6.4m.
By 1931, the population of England and Wales had grown to 40m, (400%), the population of Scotland had grown to 4.8m (270%), and the population of Ireland had shrunk to 4.2m (-46%).
The causes were:
The potato famine (which resulted in 1m deaths) in Ireland, and then decades of emigration from Ireland (much of which to England).
Certainly the Irish population has never recovered to what it was before the potato famine, but it is hard to determine whether it was ‘overpopulated’. Densely populated for a largely rural economy, and vulnerable to high dependence on a single crop, are probably correct.
To add to the top reply, given Ireland's social structure, the population level required the potato to make it sustainable. As long as the potato crop was safe, Irish peasants were better fed than many of their contemporaries. It was an increasingly precarious situation, however.
The recession that followed the end of the Napoleonic wars also encouraged a shift away from varied crops and onto the potato with no cheaper food available as a backup. These people were clustered in small holdings which further incentivised the ultra efficient potato.
Had land been better distributed, and had their diet and not been so dependent on one crop, the blight would have only been a crisis for the Irish not a catastrophic Famine.
