It's all about plausibility, and also how you write it. If you just pull it out of a hat for convenience's sake, then it's unsatisfying and probably downright dumb. Sometimes it's just mathematically impossible: Out of a city of 15 millions, it just so happens that the girl you just met is your half-sister who spent 20 years in Australia? That's when I roll my eyes and say, "Yeah, right."
If you're going to do coincidence, you need to make it plausible and leave enough crumbs for the readers to say, "Ah, now I see. Clever!"
Strange coincidences do happen in real life, but life is often stranger than fiction. In fiction, you need to take care to not take your readers out of the story by saying, "This is ridiculous."