The term ‘race’ is problematic to use when discussing the Irish and in my research I always use the term 'anti-Irish prejudice'. That said, however, the idea that the Irish were inferior absolutely predated the mid 19th century. Although anti-Irish sentiment accelerated in this period, was framed in pseudo-scientific terms (which gave it some credibility at the time), and became widespread in the contemporary press, it had its roots in the 12th century.
Giraldus Cambrensis, or Gerald of Wales (1146-c.1223) was a British royal clerk and historian who has a lot to answer for: he travelled to Ireland after the Norman Invasion and was the first non-Irish person to write about Ireland. In 1188, he wrote Topographia Hibernica (The Topography of Ireland) - a detailed account of the flora, fauna and the people of Ireland. His less-than-complimentary descriptions of the “character, customs and habits” of the Irish fascinated readers in England and Europe and really took hold, and continued to influence perceptions of Ireland and the Irish for centuries. He describes the native Irish as “barbarous” and “living themselves like beasts”; he portrays them as backward and opposed to progress; he criticises their physical appearance and clothing. His views were enormously influential and long lived. By portraying the Irish as uncivilised barbarians, Cambrensis provided justification for colonisation - suggesting that the Irish were in need of civilising and were undeserving of their land. His second book about Ireland, The Conquest of Ireland, also describes the Irish as fierce and barbarous and, like Topography, continued to be read for centuries. It is widely accepted in Irish historiography that Gerald of Wales initiated the narrative that the Irish were inferior and ‘in need’ of ruling, and his views influenced thinking and writing well into the early modern period. These sentiments never really went away and then - to skip over several centuries of complex history - intensified and became even more widespread in the 19th century.
Reading
The notion of 'barbaric' Irish was also seen in the early modern period. This term was applied to the Scottish Highlanders and Borderser too, but if you search the Acts of the English Privy Council, you'll also see the term used for different riotous groups across the English and Welsh counties. It was a word to denote an 'other' and disordered misbehaviour - in the eyes of the Southern English government and the local administration that is. Similar to the medieval period, the separation of the Irish as 'barbaric' made it easier for the English to believe they were 'helping' to 'civilise' an 'unruly' nation.
Prior the early modern period, Norman English colonisers in Ireland slowly became more Irish than English, adopting the behaviours and customs of the local people. This eventually led to further English Plantations in the Tudor period, mainly Elizabethan, and in James VI and I's regin. James dispatched many Scottish and English planters to regions in Nortnern Ireland, which is why we have Ulster Scots today. Again, these planters were used to 'civilise' the barbaric Irish people. Along with a different language and dress, the fact the Irish remained Catholic further separated them from the English. The Protestant English believed the Irish was 'heathens' and should follow the true Protestant religion. Moreover, as the English were in control, they only allowed Protestants in positions of power and they banned the Catholic Church in Ireland (which didn't work, the Irish still practised Catholicism).
A very horrid and clear example of the English believing themselves as a 'better race', or rather, a superior nation, was Oliver Cromwell's war in Ireland, also known as the Cromwellian conquest of Ireland in 1649 to 1653. This resulted in a massive depletion of the Irish population due to warfare, famine and sending people off as indentured servants to the West Indies. Cromwell's men committed massacres in Drogheda, Wexford and Waterford, amongst other places. A famous line connected to the 1652 Settlement, is 'To hell or Connacht' where the Irish Catholics were told to leave their regions for English planters to take over or they would be killed (truth in this line has been debated).
Race and nations weren't distinguished to the extent that we see today, but there was a clear separation of people depending on what country or region a person was from, and how similar they were in their behaviour or culture. The horrid notion of the Irish as 'lesser' people than the English persisted after the early modern period with discrimination in England up until the 1960s with signs in pubs stating 'No black, no dogs, no Irish'. Unfortunately, my knowledge in this area doesn't extend pass the mid-seventeenth century, but the political Irish voice became louder after this period.
An interesting book showing the Anglicisation of Ireland during this period is:
'Making Ireland English: The Irish Aristocracy in the Seventeenth Century' by Jane Ohlmeyer