Probably some Caribbean island or two which wouldn't have been one of the major sugar islands and one which they'd be lucky to hold onto for more than a decade or two. I suppose they could always request its return in peace treaties. Maybe a piece of the Guyanas if you want a colony on the mainland.
This isn't too implausible, considering how late European control was solidified over the "lesser" islands in the Caribbean. We have Courland's example as well, too. Maybe some privateers in the Caribbean are sponsered by Prussia to conquer a lesser colony, the supplemented by Prussian colonial authorities. And Prussia focuses on this one colony as much as they possibly can, which means always requesting its return in peace treaties (since Caribbean colonies always were changing hands). I think the best colony is going to be Trinidad (plus Tobago if you can), thanks to the oil reserves known since the 19th century which will mean that Prussia and later Germany will always keep a decent-sized navy.
Amusing thought--rather than bringing Indians to Trinidad as the British did, might Prussia/Germany bring in another ethnic group after slavery is ended? Bring in more free blacks (if they have something like Brandenburger Gold Coast, or something else like Germany's later African colonies), or maybe bring in Javanese and others from Dutch Indonesia?