Some time ago, I edited a manuscript that was crammed with coincidences. If the characters were searching the wilderness and got lost, they would just happen to find what they had been looking for all along. Or they walked into a restaurant and spotted a person they needed to interview. Or they found a phone that just happened to belong to a long-lost and very important relative who held the clue to solve the whole mystery. On and on it went, one coincidence after another, until the whole felt like nothing but a series of accidental adventures.
And yet, when it came time to revise the plot, we didn't eliminate all of the coincidences. I thought long and hard about it, consulted some of my favorite writers handbooks, and ultimately came up with a rule of thumb that's proved useful -- and correct -- just about every time this has come up. So here's that rule:
If the coincidence creates a complication, it can remain in the plot.
Otherwise, get rid of it.
The way to evaluate this is with a simple cost-benefit type of analysis. What's the direct result of the coincidence? Is that result positive or negative? Does it solve a problem or create a problem? Does it answer a question or pose a question? It can stay only if it's a true negative, not a mixed blessing.
This might seem like a strange way to evaluate coincidences in a plot. You might think the better solution would be to justify the coincidence by explaining how it came to happen. "He found the lost phone because the phone's owner stopped for pie in that same cafe. He stopped for pie because he was hungry, and he was in the area because he was driving from Toledo to Dubuque to visit an ex-girlfriend." The thing is, you can spin that explanation out for hours, and all it really does is slow the pace of the story by cramming a lot of backstory and exposition into the text. This isn't going to do your plot any favors. Plus, it sounds like an awful lot of rationalization, maybe even an excuse.
The trick instead is to get the reader to accept the coincidence and keep moving forward through the plot. The reader is less likely to accept a coincidence that looks like nothing more than luck. Remember GMC? Goal, motivation, and conflict, the building blocks of a well-paced plot. The C doesn't stand for coincidence, and there's no L for luck. We want to read about characters who struggle to reach objectives and overcome obstacles. We want to read about characters who try to reach a goal and fail, and fail some more, until finally through tenacity and smarts and force of will, they succeed. Not about characters who try and fail and then get bailed out of their mess by a smile from heaven.
So, if a coincidence amounts to a complication, it fits into this pattern. It's an obstacle on the path, and it's what the reader wants, so its coincidental nature will be less troubling.
Keep in mind, though, that the coincidence must still fit into the plot as a whole. It must bear some logical relevance to everything else going on in the story. That is, you don't want the characters in a contemporary diamond heist plot to get kidnapped by aliens and beamed to another galaxy. That might complicate the plot, but it doesn't fit the plot. But that's a whole 'nother issue in plotting.