What must the questioner do after having sworn by Allah to his cousin about something that the latter came to know, and then the questioner changed what he had sworn upon?

If you intended a specific type when making the oath, nothing is binding upon you unless the person accurately identifies that specific type. However, if you intended the genus of the thing and the person accurately identifies its genus, then what you swore an oath upon becomes binding, and your subsequent change of intention holds no weight; the consideration is what you intended at the time of the oath.

You are obligated to give him what you swore an oath upon (which is preferable), or you must offer an expiation for breaking an oath, and you are obliged to repent and seek forgiveness for lying.