I wish they would keep the noise down next door. - If they don't, then they don't want to.Originally Posted by blacknomi
I wish they could keep the noise down next door. - If they don't, then maybe they are unable to for some reason.
If there is noise next door, then I think the sentence with "would" is more likely.
Context would determine this, as well as the speaker's point of view. It's possible to use the sentence with "could", but I would then ask, "Why "could" and not "would"?"
Does the speaker believe that for some reason they can't keep the noise down? If so, I would say "could" is a likely choice.
Does the speaker believe they refuse to keep the noise down, or would refuse if asked? If so, the I would say "would" is a likely choice.
Despite these differences and viewpoints, one might say they mean the same thing. I tend to think speakers have reasons for choosing "would" or "could" in such a case. I would, therefore, say that there is a difference in meaning.