All literature relies on coincidence. That's because a narrative isn't a duplicate of life, it's a condensation of it, where things are brought into close proximity for maximum effect. So the audience is prepared to accept a certain amount of coincidence.
The general rule of thumb is this. Coincidence feels like a cheat when it makes things easier for the characters, illegitimately, which is to say, without them putting the work in. The detective happens to find the stolen jewel in the first pawn shop he finds. Everyone groans. But when it makes things harder for the characters, it's much more palatable. Why, of all the gin joints in all the towns in all the world, does Ilsa walk into Rick's? Who cares, it's the challenging event that sets the story in motion. The underlying reason is that we read to learn. We can learn a lot from seeing a character deal with an unlucky break. But we can't learn anything from watching someone who's undeservedly lucky all the time.
If coincidence is doing too much water-carrying for the writer, that can get annoying as well. If the writer consistently relies on improbable coincidences to put the characters in interesting situations, that begins to feel real fake, real fast. In the last Harry Potter, is it a string of coincidences that the villain is reliably able to find the hero? No, it turns out there's a hidden mechanism at work. Again, it comes down to being able to relate it to our own lives and challenges. A long string of meaningless unlucky breaks doesn't feel any more real than a long string of lucky ones.