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I am not familiar with this particular writing exercise but I have a hunch your question has to do with "could" being either imperfect or conditional for "can".

"We could not have been happier." is an example where the conditional is asked for. So the correct translation would be: Nous n'aurions pas pu être plus heureux.

Pouvoir and devoir are 2 of the hardest verbs to use in my opinion, and I almost always get them wrong. "Nous ne pouvions pas être plus heureux"  is "We could not be happier" whereas they wanted "Nous n'aurions pas pu être plus heureux" ("We could not have been happier"). Subtly different. I was more upset that one of my favourite French words of all time (époustouflante) was not accepted for the breath-taking pool (haha!)

A source of confusion arises from the fact that "could" can mean two things in English:

  1) imperfect tense of "can"

  2) conditional of "can"

Take the sentence: we could not come. It can be either 1) We were not able to come, or 2) we might not be able to come.