Okay, then... What word would you use other than "ironic"?

As far as I know, all of the things she listed in the song were things that I would have referred to as ironic, based what I thought the meaning of the word was, prior to hearing the song for the first time.

In fact, if I'd heard her lyric without knowing the title or hearing the line "Isn't it ironic", I would have guessed that the song was named "Ironic" or something involving that word.

And you can't say "Coincidence" because that's a much more mild term that doesn't capture the implied dark humor that I associate with the word "ironic". It's not about coincidences, it's about things which happen exactly, precisely, wrong... like Murphy's Law kind of wrong. To me, that's what ironic always meant, as long as I've known the word.