Someone asked me this question recently. I gave the standard, easy-to-get answer, but I feel uneasy about it because it is worse than incorrect: it is misleading. I'll try to explain, but it may be difficult to follow. On the other hand, it is a fascinating subject, a striking example of natural application of nanoengineering and photonics. First, the standard answer:
...Mammals are overwhelmingly earth-colored. A few sort-of-green mammals do exist: Tree sloths turn grayish-green when algae grows on their fur. Australia's ringtail opossums have bands of black and yellow on their hair that can look a grizzled olive drab. You could argue that a diatom-encrusted whale is green. But nonmammal tree frogs, praying mantises and parakeets are all luminous greens. Green vegetation fills the natural world, and many of its denizens use green as camouflage. Why not mammals? The short answer is that mammals are hairy. Mammalian hair has only two kinds of pigment: one that produces black or brown hair and one that produces yellow or reddish-orange hair. Mixing those two pigments is never going to yield a bright, contestable green. Rutzmoser suggests a more complex explanation: that small mammals - the ones needing protective coloration the most - typically live on the ground, scurrying in leaf litter. "Dead leaves aren't green," she points out. "They're brown."Finally, most predators of mammals are other mammals, and mammals usually have poor color vision; ergo, green wouldn't help. Given enough time, natural selection could surely produce green fur.
http://findarticles.com/p/articles/mi_m1169/is_n5_v33/ai_17338585also
http://www.madsci.org/posts/archives/2003-09/1064503150.Ev.r.html This answer is incorrect on several counts. While it is technically true that mammals have only yellow-red-brown pigments, the same applies to all but a handful of animals that make green pigments proper:
...Frogs have green rods in its retina; turacoverdin is found in the feathers of some touracos; there are green pigments in certain moths; a green pigment colouring the bug Psylla mali on apple trees is formed by symbiotic bacteria; a green pigment has been found in the integument of the lugworm, Arenicola; there are green schemochrome which color the polychaete worms Eulalia viridis and Phyllodoce viridis, and there is a dark-green schemochrome in the entomostracans Triops and Cypris.
http://www.tightrope.it/nicolaus/metadoc10.htm The rest have never learned how to produce other pigments than yellow, brown, and red, -- and some of these pigments (carotenoids) come from our food. Green lizards, parrots, and frogs are as dedicated melanin producers as the mammals. Their green originates through Tyndall scattering by microcrystals. The reflected light is enriched in blue and it becomes green when filtered by an overlayer of a yellow pigment, such as pteridine. Blue and green irises in our eyes originate through the same effect, so the mammals have not fully forgotten the trick. Cold blood animals rely on stacks of DNA base guanine in their reflective cells (iridophores) to produce this incoherent scattering effect. The birds and mammals do not have these guanine filled iridophores, as they have lost the ability to produce the stacked guanine granules. Instead, the birds make nanosize air vacuoles and channels in the beta-keratin of their feather barbs, see
http://www.nature.com/nature/journal/v396/n6706/pdf/396028a0.pdfhttp://icb.oxfordjournals.org/cgi/content/abstract/43/4/591What they do is not exactly Tyndall scattering, it is coherent scattering, by an engineered 2D structure supporting interference in just the right way, as in dichroic optics. Some birds make layered keratin/melanin thin film structures, too
http://rsif.royalsocietypublishing.org/content/6/Suppl_2/S203.abstractbut for the majority, it is air bubbles or channels lined by beta-carotene; these are thought to be produced by self-assembly.
http://rsif.royalsocietypublishing.org/content/6/Suppl_2/S253.full.pdf How did warm blood animals shed their iridophores? That's because heat trapping required covering skin, so the skill of growing purine and pterine crystals in the skin cells has been lost in the genetic drift:
...the evolution of hair and feathers, in mammals and birds, respectively, which covered the skin entirely, consequently led to the loss of iridophore expression in mammal and bird skin. Some birds retain structural colour-producing iridophores in the iris of their eyes.
http://jeb.biologists.org/cgi/content/full/207/12/2157 The birds had to reinvent color green from scratch, and this was done by inventing a way to entrap air bubbles in the beta-keratin matrix. The mammals never invented this particular approach, but they arrived at a very similar mechanism for coloration of skin (in mandrills and vervet monkeys), see
http://jeb.biologists.org/cgi/content/full/207/12/2157Their approach is coherent scattering in collagen arrays of the skin, producing blue; the birds color their skin in the same way. These arrays are quasi-ordered 2D photonic crystals.
http://jeb.biologists.org/cgi/content/full/207/12/2157Producing green skin via this approach is straightforward, and the paper claims that some marsupials and primates do have green patches of skin.
I believe that there are two likely reasons for the lack of green fur. One is purely technical: alpha-keratin of mammalian hair could be too soft for the air channel formation. Structurally, these are different proteins: alpha-keratins are helical, beta-keatins are pleated sheets. The mechanism of self-assembly that produces the "aerogel" may not work for these helical keratins, in principle. So the only way to get green/blue would be layering keratin itself. With such an approach, the problem may be in insufficient gradient of refractivity. With the collagen in skin, this is not too vexing a problem as the skin is thick, so one can have many layers, but hair is only 50-70 um in diameter, so it is hard to get an interference filter out of it, especially with the need of segregating the yellow pigment in the outer layer (to make hair green). Perhaps mammals could've developed a green pigment proper circumventing this inherent limitation, but there is another issue: the majority of mammals are color blind. Since grey/brownish coats are already providing excellent camouflage, the only incentive for green fur is sexual selection. The latter, for the dichromats, cannot lead to green fur. For the trichromate primates it could have, but they chose instead coloring their skin using collagen arrays, as chemically and physically it is easier. I speculate that the combination of these two factors is the correct explanation for the absence of green mammals. But that's just a guess.
Why there are no green mammals?
PS: How frogs and lizards make themselves green:
...Three types of pigment cells, called chromatophores, work together to make a frog green. The chromatophores stack on top of each other. Melanophores make up the bottom layer. They contain melanin, a pigment that appears dark brown or black. Melanin also tints human skin. On top of these cells sit iridophores. Although iridophores don’t actually produce pigmentation, they reflect light off of the surface of purine crystals inside the cells. When light hits these cells, they produce a silvery iridescent reflection in frogs, as well as other amphibians, fish and invertebrates. In most green frogs, sunlight penetrates through the skin to the little mirrors in the iridophores. The light that reflects back is blue. The blue light travels up to the top layer of cells called xanthophores, which often contain yellowish pigments [pteridines and carotenoids]. The light that filters through the top cells appears green to the human eye. Frogs without xanthophores look bright blue.
http://www.livescience.com/animals/060403_mm_frog_green.html ...The capacity to generate pteridines from guanosine triphosphate is a feature common to most chromatophores, but xanthophores appear to have supplemental biochemical pathways that result in an excess accumulation of yellow pigment. In contrast, carotenoids are metabolised from the diet and transported to erythrophores. This was first demonstrated by rearing normally green frogs on a diet of carotene-restricted crickets. The absence of carotene in the frog's diet meant the red/orange carotenoid colour 'filter' was not present in erythrophores. This resulted in the frog appearing blue in colour, instead of green. Iridophores, are pigment cells that reflect light using plates of crystalline schemochromes made from guanine. When illuminated they generate iridescent colours because of the diffraction of light within the stacked plates. Orientation of the schemochrome determines the nature of the color observed. By using biochromes as coloured filters, iridophores create an optical effect known as Tyndall scattering, producing bright blue or green colors. (wiki)
That's how the typical green hair mammal would look like