Well, it was mostly the way I described, but here you go:Attention, big!
Black (the hardest one to archieve):
These are all done in some minutes, so the quality lacks, but well, you get the point
To archieve the effect for any color (green red and so on), just ...
-Duplicate your animal/fur you just rendered with my aweseome tutorial, and on the top one go "Colors -> Colorize".
-Set the values to your desired color and click okay.
-In the layers menu, set the layer mode to "Color".
-Lower the opacity of the top layer as much as you want to.
-Take the eraser tool and erase some parts that don't fit (e.g. eyes and so on).
For black, this method didn't work for me, so I just went...
-Duplicating the rendered image..
-"Colors -> Brightness and Contrast".
-Tone the brightness all the way down and the contrast up to around 20 (depending on your image you might have to change this value) and click okay.
-Set the layer mode to "Multiply" or "Hue" and play around with the opacity of the layer.
-Erase some parts that don't fit.
That's the way I did this. I hope this helped, and otherwise you can just spam questions