With a post 1900 PoD, the only plausible way Japan could "defeat" the US would be if it involved a limited war, with limited war aims, in a way that a US loss would not adversely effect US strategic interests. The war would also have to be domestically unpopular. To do this, we need:
(1) The war to be started by the US, either deliberately or as a clusterfuck by misreading Japanese intentions/reactions
(2) The war to be waged over a territory not seen to be important to US interests
(3) The war involve an issue not understood or appreciated by the majority of the American people
(4) The Japanese performed better than expected and gave better than they got in initial actions
(5) The Japanese did not engage in the types of atrocities against US personnel they did in WW2
Given the above, something like the early 20th century standoff between the US and Germany in Samoa might work. Let's imagine a situation in one of the post-WW1 Pacific Mandates (either Americans or Japanese). It's early 1920. The US and Japan interpret the mandates differently, resulting in a situation in which several small atolls are claimed (or desired) by both powers. To bolster their claims and wave the flag, the Japanese detail a Kongo class battlecruiser and a few light cruisers to the area. The US responds, but lacking battle cruisers and with most of its navy still in Atlantic waters, the USN sends the old dreadnought battleship Delaware, three large armored cruisers, and a few light cruisers. The Japanese are apparently outnumbered but have the more modern ships. The Japanese arrive first and IJN marines occupy the entire disputed island chain. As the US force arrives, the Japanese ships do not respond to signals and take up formation, training their guns at the oncoming Americans. The CLs close as if to mount a torpedo attack. In response to this aggressive Japanese manuevering, the US commander oversteps his orders, and engages the Japanese detatchment. In the ensuing engagement the Delaware and one US armored cruiser is sunk, the remaining armored cruisers are damaged, one heavily, and the US force withdraws to American Samoa. The Kongo is slightly damaged and two Japanese CLs lost. US loss of life is heavy, and includes the flag officers on Delaware.. The few survivors are picked up by the IJN and treated relatively humanely.
The US claims Japan caused the war by illegally occupying the entire disputed island group, but it is obvious the actual hostilities were initiated by the US ships. Sparked by hysteria over the "yellow" peril, the US declares war on Japan, and Japan follows suit. The Anglo-Japanese alliance is still in effect, and there are some rumblings from London that the US should back down.
Immediately thereafter, the Japanese (who actually had prepared for this and hoped the US would instigate hostilities), invade and occupy other island groups that had been mandated to the US, and institute a naval blockade of the Phillipines and Guam, claiming that their aims were acheived and offering peace terms based on US acceptance of the Japanese conquests. The US refuses to negotiate and the US fleet is moved wholesale to San Franciso. In the interim there are a series of sharp actions between the wide-ranging Japanese battlecruiser squadron and US forces in the western Pacific, resulting in Japanese victories.
As the losses mount, increasing numbers of people in the US begin to question why a costly war is being waged over a series of "tiny islands in the pacific of no value to anybody". Eventually, and partly as a result of British pressure, the US agrees to a negotiated settlement. Japan agrees to return a few of the occuped mandate islands to the US, but clearly comes out ahead, both in world perception and military performance. They have beaten the US in a war.