Regardless of who I'm playing, I'm always glad to have a Thresh or Morgana in my lane. The 2 of them are so versatile and powerful, they'll work with any ADC.
On Jinx, I need someone durable with high CC that can take the hits and lock people down. Jinx is the 2nd squishiest ADC in the game, it's VERY important that nobody is allowed to sit on my face.

All of these work great with her and even an honorable mention: 
Cait is relatively safe, I'll be glad to have almost any support with me that isn't named "Sona." Particularly ones that can enhance my autos whilst shielding or sustaing, such as:
or maybe even
Interestingly enough, I also quite enjoy being paired with Annie. 
Another safe champ, contrarily I'd rather sit back and farm eventually pushing the enemy out of lane with Ricochet. With her abysmally low AS I'd rather not get into a hard engage. Someone with hard CC especially long range is nice, if a stun or root lands I try to follow-up with some heavy Boomerang Blade damage. I'll even take off-picks so long as just their presence is threatening enough to keep the enemy away:

Safe ADC #3, my whole lane I just want to farm and harass with E. Someone that can sit back and keep me safe at my eventual power point is ideal.

All of these work decently.
More important than the actual support, I need the side bushes warded or at least vision kept for Condemn picks. If someone can engage and chain-CC all the better. However, the power point won't usually be reached until at least lvl 6+Cutlass or perhaps even later.
