Out of curiosity, can I ask you why so you want this? I mean, I understand wanting a world where equality and tolerance is the norm, but I don't see the relation between that and monarchies. It could be argued that monarchies are contraproducent if you want to archieve tolerance and equality; in the 19th Century monarchs were either conservative (and thus opposed to social progress and all that) or liberal (but liberal in the 19th Century sense, that is, nationalist). So either you have a conservative force keeping social progress from, well, progressing, or you have a nstionalist one that promotes ideals of supremacy of one culture over the others.
Also, I don't see many places where a monarchy could be adopted; the world was almost completely monarchical, and the Republics that existed did largely because they revolted against a monarchy. In Europe the only republic that I can think off is Switzerland; that's an easy one to convert to monarchy: Austria intervenes in the Sonderbund War and installs a monarch to "stabilise" the country. In the Americas you must have a PoD before or at least during the Independence Wars: after a Republic has been established, if there is no past history of a monarchy, there won't be one (obvious exceptions being Mexico and Brazil, but those monarchies were established during their Independence Wars). Lastly, the most difficult countries to convert to a Kingdom would be the Boer Republics: I can think of any way to make them become a Kingdom, but if someone has ideas please share them.
Because I'm a monarchist hahaha. And about the monarchies the more I imagined in the independencias. For example the Russian Empire - we could have independence from Poland and Finnish, Austro-Hungarian Empire - Hungaria could become independent and so on, and with independence such countries could adopt a monarchy like Norway did for example.