You can't take darius in a head on fight. That's practically suicide. Your only real chance is to use someone who can either poke/farm him from a distance, or can hit and run.
If you are really looking for someone who can fight him but is still pretty cheap. I suggest jax.
The stratagy is simple. Jump in with counter strike, get some free shots in while your E soaks up most of the damage. Then once he's stunned, back away. Do this over and over again until you can go in for the kill.
DO NOT try to trade off with darius, especially after 6.