|MadSci Network: Earth Sciences|
The previous answer to this question was actually pretty good, but I'll try to give you some resources which will help you out. I'm all in favor of science fiction writers going out of their way to get the science right!
First of all, here's a planet planner; one of several "hard science fiction" tools on the web. You can input a star parameter (spectra type, mass, whatever), and calculate the luminosity for a planet with a given orbit. This will give you an idea of how bright the total radiation coming from the star is, depending on the orbit of your planet. If you really want Earth-like temperatures, you'll have to be a lot closer to the star, so I don't think the sky will be as dark as you think...
But to answer that, you need to know how much of the radiation is in the visible spectrum. The astronomer who answered the question before said that a physicist would simply use a blackbody equation which would be incorrect for K and M stars, but... Well, I'm a physicist, and I don't know any better! Here's a blackbody calculator which will let you put in a star temperature and see the wavelengths of the resulting radiation.
For a nice, cool, 3000 degree star, there is a lot less visible light, but it's still a sizable fraction of the total. If you throw in the fact that the planet must be much closer to the star to stay warm, you might find that the total visible light from the star doesn't drop too much. I seriously doubt you'll ever find a set of parameters that gives you a dark sky overhead -- even the halo around the full moon is pretty bright.
Also, remember that red light can also Rayleigh Scatter around the sky -- the scattering cross section goes as the wavelength to the 4th power. So it's less than blue, but if the blue was all gone the sky might look red or orange.
If you really want to do this right, look at this project report and contact the guy who did it. He has a ray-tracing program which can tell you the color of Earth's sky from a given set of input spectra! Pretty amazing, if you ask me.
Further complicating matters are things like molecular absorption and emission lines in the atmosphere; Nitrogen has a line at 399.5nm which contributes to the blue sky on Earth. Radiation over 700nm is largely absorbed (and re-radiated) by H2O and CO2 molecules. I doubt these effects are in the above ray tracing program.
Try the links in the MadSci Library for more information on Earth Sciences.