The Primary Valuation of Ireland 1848-1864 at Ulster Ancestry is not quite a census of 19th-century Ireland, but it's close.
This country-wide survey of property owners and households in Ireland was undertaken (of course) to determine who owed how much in terms of taxes. It is also known as Griffith's Valuation, after Sir Richard Griffith, who directed the whole effort.
The look-up at Ulster Ancestry requires entering a full or partial surname of the person you're looking for, along with the County in which they lived.
Search results provide first and last name, along with the Townland (a uniquely Irish jurisdiction, I believe, with great names like Drumreagh Otra), and Parish, along with the County name.
It's a handy, pretty easy look-up to use, and worth an explore, even with the fairly limited information that's provided with the free interface.
Also have a look at the other free Irish family history resources available here, including:
- Old Irish Names History
- 1609 Pardon List
- Mayflower Passenger List 1620
- Passenger Lists
- Censuses and Rent Rolls
and a fair number of other resources as well.
Don't forget to also check for your family history at Ancestry.com and NewspaperArchive. These are subscription databases, but they are among the most powerful research tools available for looking into family roots..