In Co. Laois, Portlaoise, Mountmellick, Abbeyleix, and Stradbally all have market squares. The latter two were towns associated w/ a large estate. Timahoe also has a village green. I think that's still officially owned by the 'big house', too. Not sure on the populations of Stradbally and Abbeyleix, but Timahoe is pretty small - though the public space is a 'green', rather than a 'square', per se.
Edit: Just looked up Abbeyleix and Stradbally's populations, and they are, indeed, less than 2,000 according to 2016 census.