Whenever this topic comes up, people often cite Japan's perceived economic "worth" as a reason European powers wouldn't try it. IMO this employs a lot of hindsight and plenty of short-sightedness as well. European colonisers tended to go for prestige as much as anything else, and many attempts at colonisation were made with absolutely zero idea of whether the territories being claimed were worth a damn thing. Africa is a prime example. Yes, Europe knew there were resources there worth exploiting, but ultimately these colonies were money sinks clung to for the sake of imperial nostalgia and, as I said, prestige. Even while knowing these lands offered little in terms of economic value they were still coveted - Germany, both in WWI and WWII, had colonial ambitions in Africa.
France's invasion of Indochina was based on its rivalry with Britain and the assumption that "land in Asia = PROFITS" without any tangible idea as to the extent, or potential lack thereof. There was also the OTL scramble for the Pacific which saw tiny islands worth only their use as coaling depots for ships annexed en masse, mostly for no other reason than "better get it before Britain/France/Germany/America does!"
I vaguely remember a timeline a while back where a longer-lasting Napoleon III steers France into Japan, and becomes "Emperor of Japan" to parrot Victoria's "Empress of India" title. It was believable; the man had delusions of grandeur and was a colonialist.
I can't say for certain what power might go for Japan. Maybe America. It would be in-character for Britain at the time, but I can only see them making a solid push for it if someone else is in Korea (or vice versa). In any case, I think a POD prior to the Perry Expedition is probably needed, but it's absolutely within the realm of possibility.