I have actually found a fair amount on the way it is calculated on Earth now. I still have to read more to understand it, but I think I have at least figured out how to use novel time scales, which is to define them in terms of angle. 1 hour on Earth (a sidereal hour) is equivalent 15 degrees around the axis of rotation. You can simply redefine an hour in terms of the number of degrees out of 360 the planet rotates in that time period. If you know the angular velocity of its rotation, then I think it should be easy to use this value in the 'normal' Earth equations.

This is very useful: http://en.wikipedia.org/wiki/Sunrise_equation

I should have known to go to Wikipedia first.