WOULD you please sit down is more like an invitation, such as the circumstance when you have a guest at your place of business or your home. But even that has a certain feel of a direct order or command, and one does not want to "command" a guest. A polite way to express the thought is ..."Would you like to sit down?" COULD you please sit down is more speculative. It is more like asking about the human possibility of an action. It is like asking someone if they have the physical ability to SIT, and therefore, it is an odd phrasing of a question. Let's look at other uses: COULD you swim as fast as an Olympic competitor? I know that I would not. WOULD you like to go to a movie with me? COULD you pay for both of us? I do not have much money right now. (Answer) I COULD pay for both of us, but I WOULD not like to pay for both of us. I WOULD prefer that you pay for yourself. Just because I COULD do something for you does not mean that I WOULD do something for you. I COULD go to that movie with you, but I WOULD never go see that type of a movie. I WOULD go to a movie with you if you COULD pick a different kind of movie for us.