i would suggest since it is a poisoners guild. that you give them links to the morag tong. from both sides.
A couple of quests I had in mind were crafting, then delivering, Treated Bittergreen Petals to a Morag Tong priest of Mephala (as a possible, maybe optional, prerequisite for Mephala's Daedric Quest), and to craft and deliver a Languorwine blade and antidote to a Dark Brotherhood contact (probably Tsrazami). I had planned to give positive Faction Reaction bonuses for the Society to both groups (that wouldn't mean that the Mournhold branch of the Dark Brotherhood would want to send you flowers and chocolates, though).
There is great potential for moral conflicts, as I see the Bittergreen Society supplying potent poisons to all sides of as many factional conflicts as possible; the player could easily find themselves helping their enemies, and suffering the consequences.