Wilcox, has a pretty good one in Union & Liberty were the US assists Californian independence during an earlier Mexican American War at the same time that Texas became independent.
A decade later when the US annexes Texas and the US and Britain go to war over Oregon, California remains independent. It is suggested that the reason was that after Britain lost Oregon it propped up a new government in California to curb American expansion. After the Gold Rush, California becomes a rather wealthy country that despite its small population ventures into controlling Hawaii and annexes Sonora out of a balkanized Mexico. As of now, the TL just began its Great War in which California (as an ally of the UK) is at war against the US (who supports a Franco-German entante). Pretty funky.
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Personally, I think the easiest way to get an independent California is to have a Mexican American war that goes awry for the US (but Mexico also looses badly). Say the US goes to War against Britain over Oregon while the War in Mexico is wrapping up.
The US already has Texas in its hands, but the situation in the occupied Mexico destabilizes to the point the US has to either withdraw with what it has (just Texas) or send in more troops and prolong the war.
The latter is not really an option as the war against Britain means the US is distracted fighting in the Great Lakes, Oregon, and the Atlantic. Part of the small force under Fremont and Kearney that established/occupied the Republic of California is called to assist in the war in Oregon.
Californio ranchers and the local militias take this as an opportunity to kick out the remaining American forces. They declare in the process a new republic, La Republica de California.
The War between the US and Britain ends up being a stupid folly that results in the same 49th parallel border (or Britain get the Columbia river border). The US would be too exhausted to attempt to take Cali again for the time being.
When the Gold Rush starts the US would then be fighting itself over slavery. By the time the US is ready to take on a new transcontinental war, California would have been independent for a full generation. And although its population would be relatively low, International interests (and perhaps even some US interests) would be against any form of annexation. As long as Cali remains friendly.
The population would be varied like OTL. And at some point California would have to establish both English and Spanish as its official languages. Asian immigration might be a tad larger than OTL, California needs the population, and traditionally Ibero integration policies tended to be more relaxed. Mormonism may or may not flourish in Cali, depending on how much it is persecuted.
If Cali plays its cards right it should ultimately enter a free trade agreement with both the US and Mexico at some point. (It could go as far as establishing a labor union as well). Some groups might think Cali is not as "independent" as they wish it to be.