TKEM, it would help to know what stain was used. I am assuming that something like Minwax Wood Finish was used but the color would help. You can stain darker but not lighter. If you can get to this pretty quickly after the original stain was applied, you can try to "wash" some of the color off with mineral spirits. Be sure to do this outdoors and leave any rags you used loose and outside for a while to dry completely.
After the stain has been on for a full day, it will be pretty well set up. No sense messing with the mineral spirits, but you can try if you wish. This may also difuse the stain deeper into the wood but not by much.
When the mineral spirits has dried for a day, apply a spit coat. A spit coat is 5 parts denatured alcohol to 1 part white (clear) shellac. Zinnser's is a good brand and try to buy the can with the newest date stamp that you can find. This will seem pretty light and you can apply it with a foam brush. Remember that the alcohol is highly flammable also and act appropriately.
It is really hard to talk about stain colors and intensity on a forum like this. Everybody sees color differently and everybody likes different colors. At this point, I would LIGHTLY sand with 400 grit or 600 grit wet/dry paper and tack rag. You do not want to break through the spit coat and you will have to recoat and sand again if you do.
Now you can use a jel stain. Hopefully, you can find something like Puritan Pine in a jel stain and you should come out with something like Ipswich Pine or a light Red Oak. Don't say anything bad about Red Oak because it's my favorite wood and stain color.
This should work OK but there definately, positively is no guarantee. A touch and experience helps a lot. The jel stain will cover a lot of the grain and stain color. You could also buy a pine board, stain it with the color used on the table and experiment. Bleaching is not something that will work or be the best answer here, I don't think.
Good luck and let us know how it is going and how it turns out. If worse comes to worse, there is always paint.