The most obvious way is to have Prussia buy the Danish West Indies from the Danes or Saint Barthelemy from the Swedes during the 19th century, because they're an up-and-coming power and they'd like a colony or two just for the prestige value. Given that neither of these entities were profitable, there's a good chance they'll get sold on to the US or Britain or France, and if everything else proceeds as IOTL Germany probably loses them to one of those three after WWI. If Prussia/Germany doesn't sell them or lose them in WWI or the equivalent, however, it can probably hold onto them as overseas dependencies to the present day, similar to the current British, French, and Dutch possessions in the Caribbean.