Thanks for the interesting and tragic question. Though it was not the area I studied in Graduate School, I have since had a long, interesting experience teaching Irish history, largely through the peculiar needs of the adjunct professor. I will look at the Ireland dimension of your question with a somewhat complicated answer. I rely quite a bit on Peter Beresford Ellis' Eyewitness to Irish History as well as Ireland: Land, People, History by Richard Killeen. I would also recommend the Irish History podcast by Fin Dwyer; he has published some books on Irish history, though more focused on Medieval history he does a good job of discussing modern history as well.

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So, first off, the experiences of Ireland is one of colonization itself; many of the practices that made English (and later, British) settlement in North America successful were pioneered (for lack of a better term) in Ireland; plantation systems, dispossession of the poor, and laws targeting the labor force the landlords relied upon in order to keep them in a repressed state. Though many invaders before the Tudors had been largely assimilated by the local Irish society and within a few generations became "Irish" themselves, the character of the colonization of Ireland from the 15th century onward was far more sustained and complete than any before. In short, Ireland was repressed to a degree unmatched in its history before. Indeed, at one point, Ireland officially becomes part of the United Kingdom.

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Irish nobility and chieftains were scattered to the rest of Europe, leaving much of Irish people without real leadership. Irish lands were given out to adventurers and settlers drawn from England at first, but later from Scotland as well. The lands captured from the Irish nobles and landowners were doled out (or sold out cheaply) as business ventures. During the Cromwellian conquests of the mid-17th century, hundreds of thousands of Irish were deported to the New World as slaves.

"About 504,000 of the Irish perished and were wasted by the sword, famine, hardships, and banishment between 23rd October, 1641, and the same day in 1652" - William Petty, The Political Anatomy of Ireland, London 1691 as quoted in Eyewitness to Irish History

At the same time, laws were passed that prevented the native Irish (mostly Catholic, though initially other non-Anglicans were also subject) from owning property in excess of £ 5, distributing land to their heirs as they saw fit, owning a gun, pursuing an education, and refusing to work for landowners.

"No Papist shall be capable to have or keep in his possession, or in the possession of any other, to his use or at his disposition, any horse, gelding, or more of the value of £ 5 or more." - Penal Code, Act 1695

Not all those who held power were Anglican (or even Protestant), but the vast majority were. Most of Ireland remained Catholic and most Catholics were powerless, reduced to de facto slavery in their own country.

"No Catholics were represented [in Dublin Parliament] and two-thirds of the seats available in the Dublin Parliament were held at the nominations of patrons for whoever could pay them the most money. No Dissenting Protestants [Calvinists] were allowed to sit in the upper chamber of Dublin Parliament..." - Eyewitness by Ellis

In short, in the period the Western Hemisphere was being colonized, Ireland was not its own master, so to speak.

But that does not mean that Ireland played no role in shaping the Western Hemisphere, or even in colonization. They actually have a wide and broad role in the New World's history. Some Irish, as I note above, were already in the New World, and working to shape and transform it. Irish were able to 'blend in' to the wider population, unlike African slaves, and occupy colonial society at nearly every level, especially if they became Protestants. Irish Catholics and Protestants alike fought in the British navies and Armies throughout the world.

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Other Irish emigrated during the 17th and 18th century to parts of Latin America, especially in Spanish-held territories where their Catholic religion was not an object of discrimination. Most prominent of these was Chile's Bernardo O'Higgins whose father had emigrated from Sligo, Ireland, to pursue better opportunities. Similarly, many Irish became important in anti-colonial movements in America, such as John Sullivan and Timothy Murphy.

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Though I don't know any particulars about Portugal, I hope you are able to see why Ireland was not really a contender in the Colonization game.