Good ADC character that's also a good support?

No such thing. Supports are all champs with strong CC and no major need for gold. ADCs rely on gold for all of their damage, and damage is what they do.

Morg doesn't do damage? Seriously? Q + W + both hits of R is something like 800 damage at level 6, as well a 2.5 secs of root and 2 secs of stun. Her and Annie are both huge damage mage-supports. Annie is better at poke, though. Karma's a good poke-support as well.

But if you really insist on it, Ashe is the one most often used for that. Jinx could as well, since she has a slow and a snare. The problem becomes that, in both cases, if they get pressure on you and you have to run away, you can't really afford to spend the time to unload your CC from either of these two, or you yourself will die.

Ashe, if you build ROA first item and keep building on HP, Armor and Mana her E passive is so OP aswell as her ultimate being a massive stun + slow to surrounding enemies.

Thresh has a very good early-mid game as ADC, if you get enough kills early he is a very dangerous champion to go against due to his harrass. Building Hextech Gunblade first item his Q, E, AA has massive damage, combine which a blitz support he has a super pull, 'Blitz pulls, takes thresh lantern, blitz pulls champ all the way to thresh' :D

Ashe, decent slows and good ult. relatively viable and good poke, just can't exactly peel.