You know your players better than I do, but... I would be pretty annoyed. Basically you're forcing them to take a terrible choice that will end up in them making a fool of themselves.

First of all, willingly accept a geas from an evil dragon is an awful choice (willingly accepting a geas from anybody is a pretty terrible choice, truth to be told). And then, the copper dragon is basically making fun of them from the moment they set foot in his lair. They face (I assume) lethal traps to get to a joke room mislead by the dragon itself to be rewarded with some magic toy because they provided the dragon with a good laugh.

After this, the next time some NPC more powerful than my character tried to set me on any course of action, I would probably just go to the beach or something to avoid embarrassing myself again.

Here you are a couple of suggestions:

The PCs could go raid the dungeon for whatever reason and after they've raid it, the green dragon appears claiming that the dungeon belongs to him. The PCs are pretty screwed now, so the dragon can offer them a deal: steal that magic item from the copper dragon and bring it to him and he won't kill them. Moreover, they get to keep the loot they collected so far from his dungeon. It's still quite railroading, but it feels better to do something you know is foolish if it's to save your life. You could add the gear spell to the deal, but if you don't and the PCs choose to break the deal you've got an awesome story arc with the dragon sending minions after the PCs and stuff, so why bother?

And then, you could have the copper dragon asking them to help with a real problem (perhaps some kobolds got into an area of his lair and he has more important things to do, so he asks the PCs to clear it for him or something) instead of using them for his personal amusement.