For the coop, build it on posts. The 'crawlspace' underneath will vary in height from one side to the other, and can be left partially or entirely open to the chickens so they can get out of the rain or sun. (It is very important that the run slope downhill AWAY FROM the coop - not just for the above shelter to work, but mostly so that a good gullywasher rain does not cause a poo-laden flood through your coop. Seriously.)
For the run, your two choices are to terrace or not to terrace. Just depends on slope and ambition. Putting down gravel or a heavy gravel-sand mix for run footing will reduce (not eliminate) erosion. Put reasonably tall grade boards all along the bottom of the run fence, to help retain the footing when it tries to wash out; make sure there is coarse gravel drainage below the grade boards so you're not creating a dam 
Simplest way to do the run fence on a slope, especially an inconstant slope, is to 'stairstep' the fence from one panel to the next. So instead of a straight line along the top of the fence, it will stairstep down, does that make sense? Other options are possible but get messy, wasteful of fence materials, and less stable, and I really wouldn't recommend 'em. 
Any other specific concerns?
Hope that helps some,
Pat