It's not clear how long this is for but you can search the census for Ireland 1821 to 1851 for free on Find My Past.
That may seem great but it's not as marvellous as you might think.
The records are only for a few counties and some counties aren't complete:
1821: Antrim, Carlow, Cavan, Dublin, Fermanagh, Galway, Kilkenny, King's, Limerick, Mayo, Meath.
1831: Londonderry (Derry).
1841: Killeshandra, County Cavan.
1851: Parts of County Antrim
Most of these won't give you much useful information except to help you confirm that a person of that name lived there.
There's more information further down the search page (hint - click the chevron or arrow next to the census year).
You'll need to register if you don't have an account and sign in.