I'm sure it varies from place to place - but a couple of years back, I just turned up and joined the queue during the stated opening hours. That was in a small regional town - so maybe it's different in a bigger urban centre...or has changed in the meantime...
Maybe if you Google your local HSE County Office. They should have a link to Community Welfare Section.
A quick phone call will give you the Community Welfare Officer for your town and details of his/her "clinic" and phone number of same.
Good luck!