One way to approach your question may  be to look at opponent ganglion cells responses (with their species specific photoreceptor inputs).  For an overview of color vision in animals I would refer you to Dr Gerald (Jerry) Jacobs book: Comparative Color Vision (1981).  He has a long career studying color vision (and pigments) in a variety of species

Here are just a few papers:

Neitz, M., Neitz, J. and G. H. Jacobs (1991) Spectral tuning of pigments underlying red-green color vision. Science, 252, 971-974.

Jacobs, G. H. (1996) Primate photopigments and primate color vision. Proceedings of the National Academy of Science USA, 93, 577-581.

Jacobs, G. H. and J. Nathans (2009) The evolution of primate color vision. Scientific American, 300 ( #4), 56-63.

Jacobs, G. H. (2009) Evolution of colour vision in mammals. Philosophical Transactions of the Royal Society B, 364, 2957-2967.

Another organism modeled well with complementary colors is the honeybee:

Backhaus W, Menzel R Color distance derived from a receptor model of color vision in the honeybee Biological Cybernetics , 55, 321-331, 1987

Thanks Carl. It's been a long time since I'd read any of Jacobs' papers (and a long time since I poked around in the color vision world); I'll check them out. 

Fantastic Olle! Of course I'd birds in mind, so my hopes for "easy" solutions are dashed, but these references look great...thank you so much! Peter

There is one study showing opponent neurons in the quail. "Matsurana and Varela 1982. Color-opponent in the avian lateral geniculate: A study in the quail (Coturnix coturnix japonica). Brain Research 247:227-241". 

However, if those turn into perceived opponent colours or not is not clear.