Probably a bit too pedantic; but it's late and I've been drinking some nice wine ...
Fowler's 'Modern English Usage' says this: 'Irony is a form of utterance that postulates a double audience, consisting of one party that hearing shall hear and not understand, and another party that, when more is meant than meets the ear, is aware both of that more and of the outsiders' incomprehension.'
That's about right, imo. I like how it's put, too, and hope others might as well. Fowler is still a treat after all these years.
Note also, 'For practical purposes a protest is needed against the application of 'the irony of fate' or of 'irony' for short, to every trivial oddity ...' I suspect Fowler would subsume the coincidences offered above under 'trivial oddities'.
I think it would be a shame if we lost the 'double audience' notion, so I tend to agree with the need for a protest. Quite right, Arfarfanarf, nothing to do with coincidence!
(Though, of course, language is alive and meanings change over time.)