I would predict CSA independence after Lincoln loses the 1864 election, with the Democratic Party going into decline, probably dying out when the Populist Party emerges in the 1890s. The US slowly recovers, and then builds up its strength, with a standing army of 200,000 and a rapidly expanding fleet, mostly monitor types unable to travel far but enjoying superior armor and firepower.
Great Britain has historically had a great reluctance to field a massive army in time of peace, having only six divisions available in early 1913, only doubling this then in time for WWI.
Given some other tension, perhaps over CSA plans in Mexico(and does this clash with or aid France), another war erupts about the 1890s. The US army smashes all into Western Canada and Southwest Mexico/CSA, while the fight at sea proves alarmingly even. Given other situations(South Africa, China, etc), the lack of allies and the growing realization of just how few nations really like London, Great Britain accepts a disadvantageous peace, hoping to appease the US this way. All of Canada west of Ontario goes to the US, along with Baja California(rendering any CSA Pacific ports useless) and probably parts of the CSA. If Kentucky was lost in 1864, no doubt London has many words about territorial concessions under duress coming back to haunt. Otherwise Oklahoma and Arkansas.
By this time US naval buildup has probably frightened London because they can't compete successfully against the US AND Germany.
And if the US never got Hawaii and such, Japan has no real interests in the US and vice versa.
Of course, if the 1895 War lasts a little while, to the crisis in China and the Boer War, then the US might actually be able to score a clear victory!