How would you guys build a green draconic sorcerer? Poison damage totally gets the shaft.
True. But, again, the definition of the dragon (though we tend to boil it down as such) is not its breath weapon. ALL dragons have breath weapons. It is what they represent and what they do with them that make a Green dragon "green"...if that makes sense.
For a green draconic sorcerer, I'd be looking at, sure poison and gaseous stuff is great...but also, more importantly, manipulations, confusions, emotional control/alteration. Charms, dominations, probably some illusion. The sorcerer spell list is RIFE with possibilities for this. Less rife on the sorcerer list, and requiring some DM intervention/approval: vegatation/forest/woodsy stuff.
Cantrips: Poison Spray, Friends. Maybe ask the DM to let you have Druidcraft and/or Thorn Whip instead.
1st: Charm Person and Disguise Self immediately come to mind. Fog Cloud and Sleep would be good here as well. Ray of Sickness if you want to play up the "poisoning" of the target. Entangle is the obvious choice if the Druid list is on the table. Detect Poison/Disease could work.
2nd: Crown of Madness and/or Detect Thoughts are a must. Gusting Wind, Misty Step, See Invisibility, Phantasmal Force, Suggestion are all good. Lesser Restoration and/or Protection from Poison from the Druid list to lend the "control of poison" angle or Barkskin and Spike Growth for the vegetation/forest thing.
3rd: Fear, Gaseous Form, Stinking Cloud (possibly, if you want the "AOE damage spell", do like I said for the black dracorcerer, add a 4d6 of poison damage on top of the sickened condition), Hypnotic Pattern are all no-brainers here. Plant Growth and, maybe, I'd go with Conjure Animals too from the Druid list.
4th: Blight, Confusion, Dominate Beast, Greater Invisibility all strike me as imminently "Green Dragon". Druid list gets you Grasping Vine and access to Hallucinatory Terrain (Blight, Confusion, Dominate Beast are on the sorcerer list anyway).
5th: Cloudkill, obviously. Dominate Person. I don't really see anything from the Druid list I would take over these two...Tree Stride might make a nice 3rd option.
So, yeah, being a Green Dragon Sorcerer isn't necessarily about flinging poison damage around all of the time. Be sneaky. Be creative. Be manipulative. If they don't do what you want after all of that...poison 'em.