If your company is in the UK and he is working in the UK, the position is very clear - he needs to apply for a UK NI number and you are required to operate PAYE. It is made clear here.
http://www.hmrc.gov.uk/nic/work/ni-uk.htm
There is a double taxation treaty with Eire so he won't pay tax in both countries - he pays it here.
Given the state of Eire and its recently increased direct tax regime, he's probably financially better off being taxed here.