Steve Costain replies: I would use epoxy mixed with Trans-tint dyes.
Jim Seroskie replies: I have used 5 minute epoxy mixed with a drop or two of Trans-tint dye (black) with great success. The epoxy can be scraped and sanded after 15 minutes or even after it is cured. If the hole is all the way through, you need to tape the bottom or the epoxy will find a way out. Fill about one-third to half, then fill last pour to sit proud of the finished surface a little.
I have seen where some will mix three globs of epoxy—untinted, tinted with brown or amber, and tinted with black. Fill the hole with the untinted then mix in the other two with a skewer to match the appearance of the original knot.
One caution—the epoxy heats up a little as it sets up causing the wood to give off numerous tiny air bubbles into the epoxy. You can break them by blowing heat with a hair dryer or heat gun before it solidifies. Use care because as you heat the epoxy, it will turn watery and you can easily blow it out of the hole.