I can vouch that the most difficult champions for Darius to deal with, 1v1, were Vlad and Riven. Riven less so, but she was still much more of a pain than other melee since she could afford to be aggressive without risking herself too much. Vlad completely voided a lot of damage, kept a strong ranged harass game going, and has a deep health pool. He's definitely one of the most directly contradictory champions vs. Darius.

On that note, anyone with a heal, or even the summoner spell Heal, are a huge pain. I've wasted many an ult and effectively been neutered by a well-timed injection of health.