As another poster pointed out, elsewhere "postal code" is usually used. The format differs. In some places it might be 4121, somewhere else it might be SW1A 1AA. In the ROI, there are no post codes.
Driven primarily by frustration with foreign companies expecting post codes - the postal service was late to computerising which paid off in having better OCR/address lookup when they finally did so actually said they were pretty indifferent to the implementation of postcodes.
I have to say my experience with posties in Ireland has surpassed my experience with postcodes. I feel like the most valid "post code" would just be the name of the postman they should ask if they're not sure.
But I have to call out Ryanair in this context. For many years, before eircode, they demanded a postcode on their payment page. An Irish company, serving Irish customers, demanded postcodes when most the country didn't have them.
(And I paypal still believes my postcode is null. I don't recall ever entering that, so I wonder where/when it derived that.)
When I got a (remote) Irish jobs a few years ago I had to fill in a post code at my tax service and a few other things, and I also had to fill in an address in the format of "street number". This makes perfect sense in the Netherlands, and I can't really blame Dutch folk for not knowing that Ireland doesn't have postal codes and that not all houses have house numbers (but rather house names).
