I'm not necessarily looking for a single one, but the least amount of it, especially outside of Japan; Japan may get a better time doing a less astringent Sakoku, though it should not affect history outside of its region as much as it can help it.
Getting the US not to buy Alaska is not too hard; just have Seward's Folly struck down by Congress or the US losing the Civil War in the first place. IOTL Russia has already considered Alaska to be a frozen wasteland not worthy of keeping. The UK is the one wild card here, but I still doubt that Russia would ever sell Alaska to an adversarial Britain. Now the real elephant in the room is how to give the Japanese an incentive to be interested in Alaska, especially when they were more interested in expansionism in Asia than the Americas.
This is the perfect answer, seriously, it is also far enough back that it could be considered a condominium in which the Japanese slowly become more involved with the administration of and come the presumed Russo-Japanese War it could become fully Japanese owned, maybe the panhandle and some other bits could be used in trade with Great Britain (on behalf of Canada and maybe Australia?) In some form of horsetrading over post-WW1 spoils, etcetera.
Does Japan have the amount of gold that will be acceptable to the Russians though? And won't Alaska be largely useless anyway as the Russians largely control the way there with their possession and development of the ceded islands?
On this topic, I had in mind a concept similar to @The Gybson Boy's The Chrysanthemum Under the Cross: Christian Japan's Timeline, this POD might be too early for the liking of OP, but anyways, here is what I have in mind:
The Yellow Peril would be kicked up to 11, ignoring that Alaska is an isolated backwater even after the discovery of gold. The Japanese population in Alaska (Arasuka?) today would be at most a few million IMO.
Current population’s just below 735K, so a couple million would actually be quite impressive.
I’d say: maybe give Japan earlier successes in its conquests.
If we are going for a pre-19th century POD (like in my Roman Catholic Japan timeline, or an earlier unification of Japan and successful invasion of Korea in 1592 like how @Rafi_T said), then a non-European country adopting Christianity, becoming an European-allied overseas (therefore, not counting the Kingdom of the Kongo and Ethiopia, who were Christian empires, but had no overseas colonies), colonial empire in the 16th century, and industrializing way earlier than OTL, would result in a considerably less racist world than OTL, since non-Whites would have had imperial powers with equal standing with Europeans as early as the beginning of New World Colonialism itself, and also predating the 19th century wave of Nationalism, New Imperialism, and "racial science" by over two hundred years, of course not even counting the butterflies that a 16th century Empire of Japan would have caused throughout the rest of the planet.
I would think that the resources that Alaska has to offer would offset a lot of the initial instability of the Meiji Era of Japan like logging, fishing, mining. Meaning they won't strapped for resources like in OTL.
