If UPS is enabled, then something must be provided in the zip/postal code field. If the shopper is in a country that doesn't use postal codes, then they can just put something else in that field.
You can modify the text label that appears next to the zip/postal code input box (you can find this text setting in Preferences -> Store Text -> Shopping Cart, I believe) to instruct shoppers in countries with no postal codes to us 'not applicable' or 'none' or something similar in the field so that they can proceed with the Checkout.
Thanks - I managed to suss that little issue out after all. I changed the pop up error message to read 'enter 000000 if in Ireland'. This seems to be the best way to overide the request. It wouldn't take N/A.