You will need at a minimum a postal address in Ireland and some form of evidence as to your right to the name in Ireland - for example a company regisred in Ireland or a name registered as a business name with the Companies Office in Ireland.
I may be wrong, but when they say that invoices showing trade to or from Ireland they are looking for a bit more than a few sales to consumers here, what they are looking for is a substantial connection to a market here, and that would be one of a number of requirements rather than being sufficient on its own.
So if i was to provide them with all my invoices to customers in Ireland, would that be OK. I have peopably sent about 40 orders to the RoI.That may be sufficient under the 'substantive connection' aspect of the requirements. But the decision is really up to the IEDR. In the past, their decision making process has been downright weird. However the IEDR has become a lot more business friendly in the last few years. The domain name would probably have to be the same as your .co.uk or .com version (assuming it has not already been registered in .ie). Anything significantly different would either not be allowed under the 'substantive connection' type registration.
The link on registration policy for .ie is below.
[iedr.ie...]
You will have to go through a .ie reseller to register the .ie domain though. The documentation will have to be submitted to the IEDR so the registration will be a more complex one than the usual.
[iedr.ie...]
The whole "reseller" concept is a legacy solution that the IEDR employs. These "resellers" typically occupy the registrars position in the normal registry/registrars/resellers chain of the domain business. Contacting IEDR directly is not the best way of going about this. They probably will refer you to a reseller to register the domain.
As part of the work on producing statistical reports on the Irish hosting business, I have to analyse .ie registrations. There is a number of UK/US/EU businesses with .ie registrations and it is not as uncommon as it would first appear. Some of it is the typical Intellectual Property landgrab of large corporations protecting brands and trademarks but there are other registrations of companies from the UK doing business in Ireland.
The number of com/net/org/biz/info Irish domains is higher than the number of .ie domains. However due to the predominantly business orientation of .ie ccTLD, having a .ie when doing business in Ireland is useful. It also allows you to have a dedicated .ie website that will appear in the "pages from Ireland" results in search engines.
And the Companies Registration Office has the rather obvious url of [cro.ie...] :)
Regards...jmcc