Can someone tell me how to do this? (Or if it's even possible)

you could make so when you have the armor on it gives you the hero of the village effect witch makes trades cheaper

Like someone69 said, closest thing to this would have to be applying the "hero of the village" effect when wearing the armor.
 

I recommend making it a full set bonus though, otherwise, player would just make boots to get the effect. 

Villager trades are kind of hardcoded into the villagers. I can think of a couple ways around this, with varying amounts of annoyance:

• Just give the Hero of the Village Effect. (Though this has balancing issues, and will also cause villagers to throw gifts at you constantly, as it's intended to be a temporary boost.)
• Mess around with NBT data commands. Using data commands, you can alter or merge NBT data- if the trades are stored as such, (and I'm pretty sure they are), you could possibly modify them using procedures that execute commands, though this would be by far the most technically challenging option.
• ...And if you've really got a lot of time on your hands, you could just rewrite the entire trade system from scratch, and override the existing GUI. Ironically, making an alternate version of the trade GUI, or just adding additional trade GUI that requires emerald equipment would probably be less time consuming then the second option.

...Of course, since Emeralds are extremely easy to obtain, they might be better off with other ambient effects. Say, being weak but increasing EXP gains, decreasing energy expenditure at the expense of armor, offering ambient potion effects, etc.