Read through this. You might pick out a tip that really help you. Think about your run too. It needs to be dry if you can manage that.
Pat’s Big Ol' Mud Page (fixing muddy runs):
https://www.backyardchickens.com/web/viewblog.php?id=1642-fix-a-muddy-run
I also have an 8’ x 12’ coop that has an open floor, but it’s the end of a long shed I closed in. The supports are different. Still, a lot should be similar.
There are two basic things you are trying to do. Keep as much water out as you can to start with, then get any water that happens to get in out of there.
First, think about where it is located. It needs to be as high as you can get it, someplace where water drains away from it, not toward it. Avoid putting it in a low place where water drains to it and stands. If you can put it where water drains away from it instead of toward it you are much better off. A lot of this depends on the slope of your land and what your options are. Just do the best you can.
Use berms or swales to divert rainwater runoff. Slope your roof or use gutters and downspouts to get water away from the coop and run. Have enough slope on your roof so water runs off instead of stands. Standing water will not only rot a roof, it will leak through. There is a reason houses have sloped roofs.
Have a roof overhang and put your vents under that overhang as much as you can to keep rainwater out. If you have a specific direction your rain normally comes from, don’t have vents on that side or use shutters or something to keep rain from blowing in. You need lots of ventilation. Roof vents and good gable vents can really help with that. Ridge vents move a lot of air but may be blocked by snow so don’t rely totally on ridge vents for your ventilation if snow is a problem.
I filled the bottom of my coop with a few inches of dirt before I added any bedding and cut a swale upslope to divert rainwater runoff. It’s worked out pretty well.
If water gets in it needs to be able to get out, whether rainwater blowing in or from runoff but stop runoff is you can at all. I know that is your question. Your coop needs to be high enough so the water has a place to drain to. Position the coop or build the floor up so it is higher than surrounding ground. The water has to have a place for gravity to take it. A lot of people use sand to build it up because sand drains so well but by using regular dirt the first few inches I’ve been able to keep water from running in to start with.
Sometimes some rainwater does blow in through my vents. With it being a bit high so it can drain but especially by having lots of ventilation, it doesn’t take it long to dry out. The chickens scratching in there helps stir it up so it dries faster.
The main thing is avoid a low spot where water drains to it and stands. That is really important. Everything else can be managed with a little forethought. If water naturally stands there though that can be really hard. Good luck!