Gunslingers are an early-midgame comp that can transition into late-game if you get lots of debuff items. The damage carries are Lucian, Jinx, and GP. You'd have to stack one with items for them to have a chance at carrying your damage and it's often outdone by guaranteed AoEs like Sorcerers or powerful bursts like Assassins. Also Rangers and Blademasters (Draven/Aatrox) will outdamage your carries as well.
Gunslingers late game are entirely dependent on things like hush, shrink, and disarm. If you're building standard carries vs standard carries, Gunslingers will often win early game but fall off. Using GP to transition into blademaster is a common option with Gunslingers since his on-hit abuse is great with barrels and even his base damage is good. That way you can get that hypercarry damage from Aatrox or Draven without ditching your gunslingers.
Overall I'd say Gunslingers are good but there's plenty of ways to beat them. Dragon is obscene in general since Shyvana and Asol can carry comps on their own and Pantheon has a great setup ult and is potentially the tankiest unit in the game with 3 Guardians. Honestly the most success I've seen into dragons are often Assassins or Blademasters that are well geared, you need lots of physical dps to chunk the durable units over time and to try and elminate the Shyvana/Asol rapidly.
Edit: Just realized you mean the dragon mob and not the teamcomp lol. This is still kinda relevant, you'll want big damage and the blademaster transition rarely fails for that. Debuffs can help as well, but given the way Gunslingers play is by splitting their damage and debuffs around having a single target is bad for them unless you have one built to carry. Red Buff on at least one of your slingers is the easiest solution since you'll get % damage.