Once upon a time I painted half of the Cottage ceiling with a primer that I tinted with some leftover green paint.
It covered the water stains.
The other side of the Cottage was painted with a coat of Kilz and 2 coats of paint. Unfortunately the water stains would not be covered.
I found a gallon of paint which I had previously mixed with primer (I use Zinsser) and the same green paint. The tenant rolled it on over the still-stained ceiling and it covered nicely.
Hope your New Year is bountiful.
What one change are you making in 2017?