First, you specifically say two carries can't go together, but listed Ashe as a great lane partner. I'm confused.
Second, the answer relies very heavily on who he is going up against. It's never black and white.
Third, you state he plays well with people with CC. You've answered your own question. Second point aside, any ADC or damage heavy bruiser works well with some form of control. In Darius' case, it allows him to get in close and start dishing out the damage while limiting the amount he takes in doing so.
Fourth, when duo-laning with Darius, it's not unheard of to play him as more the 'tanky-support', while the person you are in lane with is your carry. You can pull them in, slow them down, do a bunch of damage, and can finish people off if your adc was out of position and they run.
Lastly, he is much more a solo champion during the lane phase than a duo'ing champion. That is to say, he excels in those situations more-so than a duo lane.