The ones that I am most familiar with are for tying historical events to years. They can be found in vast numbers on websites like these ones and in exam study guides.
I'm not sure about "generally accepted"; some are probably more widely known than others. I would not be surprised to observe patterns corresponding to the (schools) of traditional Japanese arts, where the _goroawase_ students learn can be linked to geographical location/study guide used/target school/etc.
I am personally fond of the variants on "naku yo uguisu" in your example (e.g. "haku yo uguisu", "the warbler vomits" for 894, etc.), and of course "Iroiro sankyū, Porutogaru" for 1639 when Japan's ports were officially closed to Portuguese ships.