Pine is full of pitch (rosin or tar) and stain alone will never adhere to these areas. The knots are so dense and hard there is no grain to hold the stain in place
To fix, sand the table lightly with 120-grit sandpaper and restain the table. To improve adherence of the stain, mix 2 parts Gel Stain with one part Gel Satin Topcoat. Apply as many coats of the mix as needed to obtain the desired color, allowing 24-hour dry time between coats.
Note: The stain may never adhere well to the knots because they are too dense to hold a stain. You can try dry brushing the knots with the stain to deepen the color and the protect with topcoat.
Note: Pine knots will always continue to bleed through a light paint. You must incorporate the knots as part of the finish design.