"I like the Irish entry."
Translation:Is maith liom iontráil na hÉireann.
That should be acceptable (e.g. for an entry representing a particular Irish county in an international contest rather than an entry representing the entire nation of Ireland).
Because the article "an" is "na" (in the genitive case an becomes na before a feminine noun, which all countries bar Sasana are) in "iontráil na hÉireann" so it's repetition (somebody else can offer a better explanation!)