Under the provisions of the Irish Nationality and Citizenship Act 2004, children born of certain foreign national parents on or after 1 January 2005 are not automatically entitled to Irish citizenship.
Foreign national parents of children born in the island of Ireland on or after 1 January 2005 must prove that they have a genuine link to Ireland. This will be evidenced by their having 3 out of the previous 4 years reckonable residence in the island of Ireland immediately before the birth of the child. On proof of a genuine link to Ireland their child will be entitled to Irish citizenship and can apply for a certificate of nationality.
http://www.citizensinformation.ie/en/mo ... scent.html
if your wife cannot provide evidence of residence in ireland for the 3 out of 4 last years before the birth of your child, then your child is not entitled to irish citizenship.
However, if you child was born in ireland and resides in ireland for 5 years, the child can apply for naturalisation and get irish citizenship that way.