They had some smaller ones. Groß-Friedrichsburg at the centre of the Prussian Gold Coast in modern day Ghana was a colony that lasted forty years there during which time was primarily for the purpose of extracting slaves to be sold in the west indies along with a handful of other forts in the regions. The Prussian Gold Coast was then largely abandoned and the land sold to the Dutch by the Prussians.

Then in the Caribbean what is today St Thomas', one of the US virgin islands, was for the same short period they leased the island from the Danish where it formed the other end of their slave trade as a major slave market both supplying the slave worked plantation economy on the island itself and selling slaves to be brought to nearby islands. At the same time as their colony in Ghana was sold they ended the lease on their possessions in St Thomas allowing the Danish to retake full control of the islands. Again there were a handful of other islands in the region where the Prussians had some interest but small scale stuff for the most part.

As much as Prussia was a successful European State its geography didn't place in the best place in regards to being a major coloniser. Firstly, Atlantic access. Its not a coincidence that most of the great european colonial powers, particularly prior to the scramble for Africa, had fairly direct access to the Atlantic or at a minimum the North Sea. Firstly, this means that the country's ship building industry and maritime trade right from early on in the colonial period was well geared to dealing with Atlantic conditions and so it wasn't as much of a stretch for them to move to be producing ships suitable for trans-Atlantic voyages and trips down the coast of Africa and round the cape to destinations like East Africa, India, South East Asia, Australasia ect. Secondly having good and direct access to the Atlantic makes it harder in times of conflict for a country to be cut off from its colonial holdings with the steady supply of profitable exports and supplies and people heading out that is required to keep such colonial empires afloat. Prussia with its marine access being primarily to the Baltic was in a position where should it find itself at war with the Scandinavian nations that controlled the access to the Baltic it would be in a difficult position to prevent its shipping from being raided by them. Even other additional powers with large navies would have been able to exploit such a weak point to prey of Prussian shipping, generally giving them a harder time in this regard.

Then you have to consider Prussia's position as primarily a land based empire. It was always the Prussian army who's might was famed and not the Prussian navy. Prussia was too much in the midst of too many other competing powers which they had to contend with primarily on land such as their Austrian Rivals to be able to spare enough resources to to invest heavily in colonial ventures in far off locations. Countries like Britain had a fairly easy time of avoiding its political energies and material resources being sucked in to be entirely focused on having to protect itself from land invasion in European Wars hence it had the luxury of being able to invest more attention in things like colonial ventures in addition to its early industrialisation.