You can claim Child Benefit of €130 per child, per month. It may take up to six months to process but you should get arrears.
The closes equivalent to Working Tax Credits in Ireland (dont be confused with your yearly tax allowance which is called "Tax Credit") is Family Income Supplement. To receive this you need to work 19 hours per week (or 38 hours a fortnight), you can combine your hours with your spouse. You can claim 60% of the difference of your salary and the amount shown below depending on the number of children you have.
1 child - €506, 2 children - €602, 3 children - €703, 4 children - €824 per week.
http://www.citizensinformation.ie/en/so ... ement.html