I read in a book that in a situation where you are asked to join a club activity so politely that you cannot turn it down, “Could you join us?” is more polite than “Would you join us?”. Why is that? I’ve never thought which is more polite.
There is not much difference, if any, between using "could you" or "would you" in a polite question.
In other contexts, "could" (as the past tense of "can") expresses possibility or ability, whereas "would" (as the past tense of "will") expresses intent or certainty. The implied certainty of "would you join us?" may be a little bit more demanding (and thus, less polite) than "could you join us?". That is most likely why the book made the distinction it did.
In practice, however, especially in spoken conversation, there is basically no difference between the two, and the perceived politeness will come from your tone rather than from your choice of words.