In recent years there has been a trend towards introducing the term 'Northern Irish' in a variety of situations to replace the traditional 'Northern Ireland'. For example, some people refer to the Northern Irish economy, whereas traditionally we spoke about the Northern Ireland economy.
It seems to me that the traditional form is better because it is clear that it is referring to the country of Northern Ireland whereas Northern Irish is somewhat ambiguous. Moreover, from what I can recall of English grammar, the use of Northern Ireland in this way is in fact as an 'attributive noun' ie a noun that modifies another noun and is optional - meaning that it can be removed without changing the grammar of the sentence. Although I wait to be corrected by some 'experts' in grammar!
Since it is grammatically correct and avoids any possible ambiguity, I will therefore continue to listen to the Northern Ireland news, enjoy Northern Ireland culture, work as a Northern Ireland politican and hope that both the Northern Ireland weather and the Northern Ireland economy improve.