Mammals don’t come in green. We have 2 colours available to us, in different amounts: eumelanin, which is dark brown to black, and pheomelanin, which is yellow/red. We can mix those up in any way, or none (for white), but it’ll never be green.

Now, many other animals don’t have green either, peacock feathers for example, have brown pigment, but they have a structure that makes it look green and blue from wave interference.

Unfortunately, you can’t really do that with fur, since you need to look at fur from all directions, not just the front.

So, mammals don’t get green fur.