This question is answered in depth on the following web page:

How can I tie-dye bean bag toys or other stuffed animals?

To summarize, it all depends on what fiber the outside fabric of your plush wolf toy is made of; most stuffies are covered with particularly hard-to-dye synthetics. It's easy to dye wool or mohair, or silk, cotton, or rayon velvet, but the synthetics can be a major problem. If it's polyester or acrylic, you might be able to dye with with a special polyester dye called disperse dye, but that requires extensive boiling, which might ruin the fur. Instead, you could use a good thin fabric paint like Dye-na-Flow or Dharma Pigment dyes. Or, you could find a pattern for sewing your own wolf toy in any color that you like.

I'll bet that there are people out there who will sew a custom-designed plush toy. It's almost impossible to find anyone to dye anything that is made of polyester or acrylic, though. For that question, see "Where can I find someone to dye my clothing for me?".

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