Using Coincidence in Your Writing

It's enormously challenging to find ways for the main character to learn new information without the story events seeming too coincidental. My ideal way to write a story would be to avoid using plot devices that are too convenient. And to especially avoid these devices at crucial moments in the plot. The reader expects surprises, but they need to be believable and flow naturally from the story events.

One thing that helps me with this issue is to think about what the minor characters are doing when they aren't "onstage" in the scene. These characters pop in and out of the story, and may play a crucial role at some point, but as a writer, I need to think about what they're doing when they aren't with the main character. Otherwise, dropping them in just when they are needed can seem too coincidental.

How do you avoid coincidence in your story?