In 1971, the U.S. and Japan signed a treaty reverting Okinawa and the surrounding islands back to Japanese control, which stated "the United States of America relinquishes in favour of Japan all rights and interests under Article III of the Treaty of Peace with Japan signed at the City of San Francisco."
China points to its own agreement with the United States, the 1943 Cairo statement issued by Winston Churchill, Franklin Roosevelt and Chiang Kai-shek. The three leaders agreed that following the war, "Japan shall be stripped of all the islands in the Pacific which she has seized or occupied since the beginning of the first World War in 1914, and that all the territories Japan has stolen from the Chinese, such as Manchuria, Formosa, [Taiwan] and The Pescadores, shall be restored to the Republic of China." If you accept, as Beijing does, that Diaoyu was part of Chinese-ruled Taiwan prior to 1895, then that would indicate that it would be returned to China along with the other seized islands. (It would also mean that the U.S. military was bombing Chinese territory throughout the '50s and '60s, but that's another issue.)