Garen Beats Darius Hands Down
While Darius is a well known lane bully with a nice heal on hit effect, I would argue that Garen should win this lane 9 times out of 10. Granting that Garen doesn't make any huge mistakes of course. All you need to do is follow a very simple play-style and item build for this matchup.
Item wise, rush a Deadmans first (you won't be close enough to Darius most of the time for Sunfire to be useful), then Ninja Tabi boots, and finally Black Cleaver. At this point you'll be able to consistently outtrade Darius and can itemize more for their team composition.
The actual play style consists of one very simple dance. Wait for Darius to use Decimate, rush in and Q, E, W, and rush out again. You'll use W right before silence ends and start running away halfway through your E so he can't pull you back in.
This sounds pretty obvious but I see this matchup go the other way all the time and it's because people don't follow the dance. I'm only writing a post about this because I just finished my 5th ranked game against Darius in the last week and I've made him feed in every single one of those games.
Try it out and have fun making Darius cry. : )