One way to facilitate Japanese development of an atomic bomb is for it not to be involved in WWII. Say, with the appropriate POD, no all-out Japanese invasion of China in 1937. The timeline meanders along, there's a little more money for Japanese scientists to tinker with nukes, butterflies result in slightly advanced nuclear program in other countries. Hitler goes crazy, WWII breaks out, it ends with atomic destruction. Japan is one of the countries that sees atomic weaponry is vital to be a 1st class power in the new world order and builds a weapon as fast as they can.
1945 is probably too optimistic. The Soviets did it in 1949 with the advantage of nuclear secrets and an economy that despite being devastated by war, was much larger than Japan's could be. The British did it in 1952, being screwed out of nuclear secrets and with a pretty lousy economy. So lets give Japan an atomic bomb in 1952.
This opens a possibility for a nice parallel to OTL. Maybe the Chinese decide to liberate Manchuria, and as they cross the Yalu into Korea, hardline Japanese generals press to use their atomic bombs and usher in an era where conventional use of atomic bombs is the norm...