There's an opinion that such coincidences are not coincident at all.

It couldn't just be a coincidence.

The two accidents coincided with each other.

What a coincidence meeting you here!

It was just a coincidence.

What a coincidence!

Coincidences happen all the time.

Completely coincidentally, these two are still being repaired.

Many politicians are undergoing a conversion of conscience on the subject of marriage equality, which not coincidentally reflects a shift in public opinion overall.

That's an improbable coincidence.