No cannot be done, part of the wood that will always show without covering over with solid stain or a paint.

millworkman
Thanks for the reply. I was afraid of that.

If you are really desperate to make the knots vanish, try a faux painting just over the knots that matches the grain of the knot-free areas.

Then put a clear finish over it all to protect the painted areas.

If you have some wood very similar to the top in grain and color (perhaps replacing a board that's not visible) you can hide them. Google "dutchman repair" or similar to see examples. Basically you route out the knot area using a router to 1/8 to 1/4 inch deep and replace it with a piece of clear wood. The trick is making it invisible. If you look at "clear" plywood you will see football shaped inlays that represent a bad job of replacing knots. If you use a curved, irregular shape that follows the grain, carefully matched grain in the replacement piece, precise joinery, and perhaps some touchup paint to extend grain lines across the repair you can make them nearly invisible. There was a detailed article in Fine Woodworking several years ago on doing this. Most woodworkers deal with fixing mistakes eventually, and this is a common method.