How about a catapult that fires nurglings at people? They could have little parachutes or something...
Reminds me of the old goblin Doom Divers! I have to agree, for artillery of some kind, nurgling catapults seem like the most obvious choice, unless you're trying to avoid being goofy. Given their role in the lore, though - as the vectors of disease - this seems like a fair choice. If you're looking to make up rules for them, then I would imagine they'd cause relatively little damage on impact, but disrupt units by jumping around, grabbing ankles, etc., and have the potential to spread disease of some kind.
If that's too goofy, then I think something that launches clay pots full of either poisonous gases or some corrosive contents would be ideal. Maybe look to the effects of troll vomit or something for rules.
For missile troops, I think I'd probably just stick to bows, crossbows, slings, and sling-staffs. Nurgle mutants have also often had the ability to vomit corrosive liquids in games, so units with short-range area-effect attacks might make sense.