I shade with Prismacolor markers and with Acrylic paints on a dry brush. For small areas I would use markers. To me they are not good on large areas, they make the fur feel a little sticky. Whatever type of permanent art marker you choose see if you can purchase the blender pen. It is a no color pen that blends and also can remove the color. It really works well for blending the color, I would not do without one, or two.
I have just done some shading once on a bear, but think it turned out rather cute. I used pastel chalk (is it called like that in English?! ). First, I rubbed it over paper to get the dust. Then I took a very fine tipped brush (as I work on miniatures), took some of the dust with it and gently brushed it into the fur where I wanted it to be. You could also use a Q-tip if working on a "round" area like under the eyes.
Just my 2 cents, I don't know if others do it this way too
I try whatever I can find- normally testing on a small piece of fabric before on the bear. I try and use Prisma felt tipped Pens, although I have to import them as we do not have an agent for them in South Africa. I purchased the Prisma colored pencils from Sassy bears and they seem to work nicely. Then I have also used colored chalks.
Copic Pens can leave a sticky residue, although if used with the "air pressure system" this gives a better result.
The important thing is to blend the colors and create a natural look.
For my bears I use oil - colours. Usually I put some colour on a paper and let it stand at least one hour (usually more), than oil separates from colour (you can see a fat spot around colour on a paper). I use dry brush to shade around eyes and nose. I do not shade fur, only basicl. Lot of my bears' muzzels are totaly trimmed. Hope I helped a little bit