HI
I believe that IT services, consultancy or electronic services are classified as 4th schedule services.
Therefore the place of supply is in the place where the service is located. Therefore no Irish VAT arises and you dont charge Irish VAT but the service is zero rated. The so called reverse charge applies and the uk customer must charge themselves UK VAT but they are entitled to an input credit for this UK VAT in the normal way.
You must obtain the customer's VAT number as evidence that they are a business and you must state on your invoice, the customers VAt number and that the reverse charge mechanism applies to this transaction.
Further information is available here [broken link removed]
Hope this helps
DB