For this group, I think it comes down to how the lair is set up, the lair actions, and the dragons attacking in a hit-and-run fashion. I'd set up the lair as a thorny hedge maze, rife with traps, under a dense canopy of trees. The characters would need something at the maze's center and would only have so much time to get to it before they fail to achieve their goal.
Green dragons are cunning and tricky, so I'd run the dragons where they would mostly lurk up in the heavily-obscured canopy and periodically strike out at a straggler (hopefully the cleric) with bite (10 ft. reach), tail (15 ft. reach), or breath weapon and then fall back and hide in the canopy again. The dragons would also use the grasping roots and wall of tangled brush lair actions to stymie the ranged characters and to separate the group. The magical charm-cloud lair action I'd reserve for the barbarian though the paladin's aura might be troublesome especially if it's a devotion paladin. With that charm, I'd tell the barbarian to run off somewhere in the maze and get lost for a while or put him or her on a path toward a trap. I'd probably send the young dragons in to snatch and eat the "protection from poison" items if that is feasible, then fly away.
So here we have both exploration and combat pillars in this challenge all while under time pressure. The dragon smack-talking the PCs the whole time would make for great social interaction and I might even suggest that the dragon could be outsmarted and goaded into a direct confrontation with the PCs rather than hit-and-run tactics. This opens up another path for players to take to defeat the dragon. In anyc ase, it's still likely the PCs will succeed, but I'd do my level best to make them pay for every inch of ground they cover in a fun, exciting, memorable way.
