In Rex Stout's "It's Science That Counts" (All-Story Weekly, 1916), Jonas Simmons is a small-town hardware store owner, who has acquired the reputation of being a skilled boxer due to his practice of working out on a light punching-bag in the back of his store. For years, the Annual Picnic of the Holtville Merchants' Association has featured an open challenge for an exhibition bout with Simmons — a challenge which no one has ever taken up. Then a new young clerk in Bill Ogilvy's store, Mr. Notter, starts boasting about having been the boxing champion of Columbus, and a planned bout between Simmons and Notter is the talk of the picnic.
But Simmons was never all that much of a boxer, in fact, and so as the time for the bout approaches, he panics and runs away.
At length, figuring that he had left the grove and the roped ring at least a mile behind, he came to a halt in the midst of a tiny clearing surrounded by trees and shrubbery. He glanced warily in every direction, and for a full minute he stood perfectly still, listening intently. The only sound was the cry of blackbirds from above the woods. Exhausted, panting, he sank down on the grass and stretched himself out to rest and think.
But it turns out Mr. Notter's boxing career was fictional, and so he was just as apprehensive about the fight as Simmons was:
At this point the course of Simmons’s thoughts was abruptly halted. He heard a noise somewhere to the right— no, the left. A sound of something moving. Instantly he was on the alert. He rose cautiously to his hands and knees and crawled across the grass to the shrubbery. Noiselessly pulling a branch aside, he looked through— And found himself face to face with Mr. Notter!
They exchange embarrassed greetings, and then Mr. Notter bursts out laughing:
“What you laughin’ at?” Simmons demanded.
“Oh, all them people,” the other managed to get out between gasps.
“All what people?”
“Why, back there waitin’ and lookin’ for us. Waitin’ to see a bloody nose. And here we sit, laughin’ at ’em!”
“Well, if you’re going to make so much noise they’ll soon find us,” Simmons observed. But he grinned in spite of himself. It was funny. He could see Peter Boley and Slim Pearl and the rest running around like chickens with their heads cut off.
“It’s queer we should both come to the same spot,” observed Mr. Notter presently. “One of life’s calm incidents.”
That was the way Simmons understood it at first, then he realized that the other had meant to say “coincidences.” He nodded in agreement.
"Calm incidents" for "coincidence" is not in the Eggcorn Database, nor does web search turn up other examples. It doesn't seem like a high-probability misunderstanding on phonetic grounds; but this linguistic incident, calm or otherwise, is not at all central to the story's plot, and it seems likely to me that Rex Stout threw it in because the coincidence was something that he had observed or encountered in real life.
Specifically, I wonder if there is (or was) an American speech variety in which the vowel of calm is close to the first-syllable vowel of coincidence… The eggcorn would be especially plausible if the shared vowel were rounded or had a rounded off-glide — in my speech, "comb incidents" is pretty close to "coincidence". Stout was raised in Topeka, Kansas; and the story under discussion takes place in fictional small-town Ohio.