When it comes to requests, we can use both could and would, but could is more formal and polite than would. While making polite requests, could is used with suggestions, as it indicates a possibility. On the contrary, would is used with offers or invites, because it is more usual.

Would or could for polite requests?

But I would suppose that “would” is more polite, because it expresses the idea of probability, and of willingness, and of the desire that something be done, whereas “could” is more in the realm of ability (yes I can). And according to the American Heritage Dictionary, “would” is used to make a polite request.

Could you vs Would you polite?

'Could You' indicate someone to do something in an alacrity way, whereas 'Would You' implies that someone is asking for a favor in an appropriate and polite way.