Your challenge is to have the population of Ireland restored to its heights before the Great Famine by the year 1900.
Without waving away the Famine, that's just not going to happen, maybe just maybe if you were able to utterly change the UK's politics to allow massive government intervention (which is ASB honestly) you could slow/arrest the continued migration between the Famine and 1900 but regrowing the population...Your challenge is to have the population of Ireland restored to its heights before the Great Famine by the year 1900.
Given thaat there was even a "little" famine in the 1870's even if you had low migration between the Great Famine and then you'd likely see renewed deaths then if the population was higher.Very very low emigration of Irish families after the famine.