Have Germany decide to focus on Europe and not want to colonize, maybe Germany wanting to unite all Germans, particularly the ones in Austria-Hungary and maybe Netherlands/Belgium, which mean they don't really focus on a navy outside of coastal craft. This means Britain will be more focused on France and Russia in the great game.
I think this would be the main one. Colonial rivalry was the main cause of relations souring between Britain and Germany; without it, France remains the big competitor, and an alliance between Britain and Germany (both long-term rivals of France) makes sense.
Extra bonus points if they lose WW1 catastrophically.
Let me see...
- POD 1: The American Civil War is even more bloody and protracted. A huge number of slaves flee north, dramatically reducing the black population in the Southern states. After the war, Reconstruction is a failure, and the South is populated by bitter independentists who blame the Yankees for stealing their slaves and are itching for a second pop at nationhood.
- POD 2: As above, the Germans don't seek (as big) a colonial empire. Consequently Anglo-German relations remain cordial, and the two countries form an alliance against France.
- POD 3: Russia industrialises and reforms its army better than IOTL, meaning that it's in a much better state to fight a modern war.
- WW1 breaks out over some cause, with France/Russia (the Peripheral Powers?) fighting the UK/Germany. The French, knowing they can't beat the British in a conventional naval war, try using submarine warfare to starve the island, inadvertently bringing the US into the conflict on Britain's side.
- Fighting in Europe is extremely bloody, but with a more efficient Russian army, the Anglo-German-American forces on the Continent are ground down. Germany is forced to surrender and occupied by the victorious Peripheral Powers.
- The war reaches a stalemate, with Britain and America blockading France and Russia, but unable to land a decisive blow. Unlike IOTL, the blockade isn't enough to defeat France and Russia, which have far more food and industrial resources than Germany did historically.
- The inability to gain a victory, plus the economic hardship caused by the war, causes the US government to lose prestige. The South rebels again. Its black citizens are almost all staunchly pro-Union, but because there are much fewer of them than IOTL, they don't have much effect on the war. The US hurriedly makes a separate peace to focus its resources on dealing with the crisis. Nevertheless they fail to prevent the South seceding. Consequently their strategic position is much less strong than IOTL, leaving them less able to exert power and influence in the rest of the world.
- With the US out of the picture, Britain stands alone. France and Russia are able together to put together a fleet capable of challenging the British for naval domination. The British fleet is defeated. In a panic, Britain sues for peace, paying heavy reparations. The country avoids occupation, although the blow to its prestige is severe. Rebellions and independence movements break out across the Empire, and Britain is unable to control them all. Soon it loses the majority of its overseas territory and becomes a second-rate power. The end.