Before all you kids go like "nO yOuRe WrOnG iTs sO oP," you could literally just make a wheat or coal farm (you can trade with farmers and blacksmiths, which will usually give you emeralds for a certain number of coal or wheat), and get stacks of emeralds much quicker than trying to search for a biome that's not very common to find an even more hard-to-find ore.