The way they measured this in the census is ridiculous, but anyway (2006):
Asked by which "Ethnic group" you belonged to the responses were:
Irish 87.37%
Irish Traveller 0.54% (#1: LOL not an Ethnic group, a complete sop to the worst sort of leftie identity politics that they are counted and #2 I doubt it is anything like this high anyway.)
"Other White" 6.93% (See what the problem is?)
"African" 0.97%
"Other Black" 0.09%
Chinese 0.4%
"Other Asian" 0.86%
"Mixed" 1.1%
DNS 1.73%
These are best figures I can find (I imagine Jas has better ones). But you may see the point now of the old Irish demographer joke that along with Ulysses the greatest works of fiction produced in Ireland are the national censuses.
Yes, the ethnic group thing is a shambles. It is unfortuntely the closest thing available to answer the question asked.
Tables on population by place of birth (
here) and nationality (
here) may be of some interest; and indeed the CSO's report on non-nationals in Ireland (
here *warning: large file*) which includes profiles on the 10 largest non-Irish national populations in the country.