This is a very tough assignment. The problem is that not only would the US need to radically change their foreign policy on Europe, but there has to be strategic value of the territory in Europe and a link to the USA. Sure we could have an Ottoman-American war where the US ends up with Abania, but how do they keep it?
With that being said, the only scenario I can think of is:
Spain regain Gibraltar in 1940 when Franco foolishly decides to declare war against the UK. The move comes as the British have their hands full with Germany and Italy, and like Finland, the Spanish limit their operation to only the disputed territory of Gibraltar and do not join the Axis.
In short order Franco realizes he made a tremendous mistake as it becomes increasingly clear that Germany is not going to win the war.
Franco also realizes that to simply pull out of Gibraltar would be fatal to his regime and to the Spanish psyche. He then agrees to "lease" Gibraltar as a military base to the Americans In 1942, with an agreement that a referendum to be held at a later date. This is satisfactory to the Brits since they still have a edge in population on Gibraltar and since Gibraltar is key for the upcoming operation torch.
Gibraltar soon emerges as one of the Americans most important military bases during the Cold War, and the population swells as Americans flood into the territory.
Referendum in 1957. But, like Hawaii, American soldiers are allowed to vote. Optins are:
Remain part of Spain.
Return to UK
Independence
Become a territory of US
In 1980, Gibraltar admitted to the US as 51st state, much to the anger of both Spain and Britian. But many pundits see it as a direct response to the loss of the Canal Zone.
All that is highly unlikely, and I can see any little thing throwing that highy unlikely scenario from happening. But it seems the only plausible situation with a POD after 1850 that gives the US territory in Europe.
