Late to the party here, but FWIW: The Minwax stains you can get at the hardware store aren't even all that good for regular wood. I've tried using a few, and the results on regular wood have always been meh. You're much better off with an alcohol-based dye, such as what Fiebings offers. You can get the stuff on Amazon for a few bucks. A little bit goes a long way.
I've also had some success using a water-based aniline dye, on both regular woods and briar. But the leather dye comes pre-mixed and ready to apply.
Let me reiterate some of what's been said above. You should know that most pipe makers will put at least two different coats of dye on a pipe. They put on a dark coat (often dark brown or black) and let it dry. Then they sand it back and apply a lighter color. After sanding back again and/or buffing, they'll apply a clear coat, usually oil and wax. That's how they get the contrasting colors on the grain to pop visually.
Once you dye your pipe, you will want to re-coat it with some finish. It's best to put a coat of Danish oil or some other drying oil on first, wipe and let it dry thoroughly. Then apply wax. If you go straight from the dye to the wax, you'll sometimes find the dye coming off on your hands sometimes as you smoke the pipe. The hot pipe will make the dye bleed right through the wax. The oil coat seals the color in.
