Consider this fictional character and these scenes from his life:
1. It just so happens that our character works three weekends in four and on his weekend off he just so happens to be in the same nightclub as the young woman who, just so happens, to have gone to that club for a change. That young woman would one day become our character's wife.
2. It just so happens that, feeling pretty fed up, he arrives home from work one Friday evening at the same time as his neighbour. It just so happens that this neighbour is an office manager. The chance comment of, "Have you got any jobs at your place?" leads to a new and fulfilling career for our character.
3. On the day that the character is due to transfer to a new department it just so happens that he is seconded to another area. It just so happens that this new role turns out to be better than the one he was moving to and revitalises his career.
If you take these three situations and weave them into a short story no-one would buy it. The whole thing would smack of cosy coincidence or even deus ex machina. Even if you used the scenes as part of a much larger, possibly generation spanning, novel the author might, even then, still be accused of contrivance.
The thing is, those three vignettes are actual snapshots from my life - albeit spread out over a twenty five year period. Now, I deliberately worded each of the scenes (with the liberal use of 'it just so happens') to highlight the potential charge of forced coincidence.
Coincidences do happen in the real world and we shouldn't be afraid of using them credibly in our fiction.
The important thing is to show how these coincidences could happen.
In the first scene we would explain how our character only gets one weekend off in four and it is the norm for him and his friends to visit this night club. We'd then have to show why the young woman and her friends choose to visit the club that night.
For the second scene, showing the two neighbours as friends who regularly discuss their respective jobs would foreshadow our character raising the question of a job change.
In the final situation, we could reveal more of our character's work background and highlight doubts and uncertainties about the move he was planning to make before he was re-assigned.
All three of these scenes can easily be regarded as coincidences. They can also be explained away as consequences.
It's all in the way we tell it.