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Countries don't really have nicknames, the people who live their often do however as Rats posted above (a 'mick' is an irishperson and not a nice nickname either, like calling an American a yank or a greek person a spik) they are usually unkind or derogatory.
Most countries use the name of their country in their own language - Hungary = Magyarorszag, Germany = Deutschland, - I can't really think of any more examples. Is that what you were thinking of asking?
Luck of the Irish.
Irish = backwards. Thats the most common nickname I remember.