The most convenient way to open a Euro account will be via your existing bankers as this will minimise the amount of documentation that you will be required to produce to meet legislative requirements. Your existing relationship manager will be familiar with your needs and may also be holding security or deeds to facilitate overdraft or loan facilities which may be extendible to your new account.
That said there is nothing to stop you using another bank specifically for your foreign currency business and some account holders prefer to shop around and form a secondary banking relationship.
Euro accounts can be domiciled in N.I. without the need to approach a bank in Ireland.