A series of articles worth reading on this subject.
"The Eyes Have It"
Interesting, according to that article canines and felines have cone receptors in the "red" and "blue" ranges and lack one centered in the green range (although their red and blue cones still overlap into the green wavelengths).
This is different from what I recall about deer vision, where they have cones in the green and blue range, but lack one in the "red" range which is why deer aren't supposed to be able see red light. Keep in mind that for humans, and appearently cats & dogs, the "red" cone actually peaks in yellow-green, and just barely has enough sensitivity out in the real red wavelengths to allow us to see them at all. The closest that deer vision gets is yellow-orange out on the edge of their "green" cone sensitivity. I guess they might still be able to see a red light in the dark if you shine it right at their eyes, but it would probably look pretty dim to them.
Um, but going back to the article, it sounds like what they were implying about the coyote's perception of green would be of more importance in selecting the color of your camo, and not so much the color of your leds. They say that coyotes would percieve green as being in shades of white or grey, but that means if you shine a green led at a coyote at night, they would still see it as a bright white light in the dark.
In contrast, if you shine a red led at a deer, it might be able to see *some* light in the dark (this might depend on whether it's 630nm orange-red or the deeper 660nm red), but would appear a lot dimmer than any other color.
Maybe think of it like when we look directly into a near-infrared light, sometimes a feint red glow is visible, but it's barely visible even in total darkness.