He's a lane bully.
Your best bet, I believe, is to either play a better scaling champion or a champion with better teamfighting. Don't lose lane early to mid game, but don't expect to win it against a lane bully. Depending on which kind of champion you chose, you're then free to either win your lane once you get rolling, or help your team achieve objectives (save TP for defending top if Darius splitpushes, and/or grab homeguards) and then the game.
Darius, since he is a lane bully, can and will out-damage you early and mid game. It's what he does, it's his design. Sometimes winning lane is not the only way to win the game (let's be honest here, if you're Vayne against Graves all you have to do is not die. If you can manage that, two-three items and you'll be making him your bitch).