Scripts demand causality. One event causes another event and so on. But then, is there room for coincidence? Has chance a role to play? Oh, yes!
Basically, one coincidence is acceptable per film. But there are exceptions. There are always exceptions.
Sometimes, coincidence is used as the Inciting Incident (Field and McKee concept) that makes everything happen. At the beginning of Star Wars, Leia is trying to send a message to Obi-Wan Kenobi through R2D2, but Luke Skywalker receives it instead. Our main character reads it by chance. Then, everything is set in motion through causality.
I have nothing against coincidence, it’s part of life and films are about life. We just have to be very careful with it.
Let’s talk exceptions:
Comedy. Here coincidence can even be the driving force. Feel free to use it if it works for you.
Can two coincidences be acceptable in a film which is not a comedy? Maybe. In Save the Cat, Blake Snyder complains than in the first Spiderman by Sam Raimi there are two coincidences and these, he thinks, kill the film: Peter Parker gets bitten by a spider that makes him a super being AND a person really close to him becomes the Green Goblin. Snyder doesn’t buy it. He has a point, but in my opinion, Spiderman’s case is an exception: here we are in superhero territory and it’s in the soul of this sub-genre that these things happen all the time and the audience is aware of it. But that’s just my opinion. It’s yours that counts.
More about screenwriting in Save the Movie! Is Blake Snyder to Blame?, Best Screenwriting Books: THE ART OF DRAMATIC WRITING, Best Screenwriting Books: ESSENTIALS OF SCREENWRITING and Best Screenwriting Books: Dmytryk’s ON SCREEN WRITING, amongst many other posts!