Use he shellac primer (Zisner BIN, etc). Read the instructions. Usually two coats will suffice. Dries quickly. Then you can prime again with your normal primer. The reason? The shellac primer often dries to a very smooth, slick surface. Once topcoated, it may reflect light slightly differently than the wood that's primed/painted without the shellac. Especially with a low-angle, raking light.
Shellac primer, two coats. Lightly scuff sand to provide tooth. Normal primer (same used on rest of wood), then two coats of paint.
If you're repainting the entire area, you should get excellent results, even if you treat the knots then just give the entire area a second topcoat.
If you are just touching up the knots, ask your paint guy if the paint you are using "flashes." "Flash" refers to how well a paint blends in with an already painted area. Some paints blend well after a while. With other paints the touched up areas stand out like a sore thumb.
Often times it does take a few weeks for the touched up areas to blend. The gloss difference fads over time.