I don't know about NI specifically, but there are only a few UK banks who have Euro accounts. Since I haven't posted enough to post links, you'll have to look them up for yourselves:
Barclays Euro Current account (Free to run, no interest, cheques only, payments in/out cost. Quite useless).
Citibank Euro current account (Free to run, free SEPA - they were trying to change this to £10 per transaction but were challenged for breaking EU rules, not sure of the current position. Euro debit card. No interest. Just pay the exchange rate load to transfer between EUR/GBP/USD, no fixed fees)
Citibank Euro savings account (rates up to 0.75%)
HSBC International Current/Savings accounts (interest again poor, savings up to 0.75%)
Cater Allen current account (haven't looked in much details)
Bank of Cyprus savings account
Lloyds euro current account (I think they have one)
A few other banks have business banking accounts in Euro. None are very special.
For current accounts the Citibank account stands above the rest. If you want to avoid paying a SWIFT fee (£20-40) for moving money in and out it's the main one to choose.
For savings accounts Citi again probably wins, though the rates are dismal. Bank of Cyprus might have better rates, but they aren't shown on the website.
Citi (being a global bank) might be open to RoI residents - you can always ask.