The Despotate of the Morea, which was a province of the Byzantine Empire, looks like one of these at first glance, but it isn't. The words "Despot", "Tyrant" and "Dictator" have all changed their meanings over time.
- Despot was originally the highest rank of the court of the Byzantine Empire, bestowed on close relatives of the emperor (the modern concept of prince didn't exist at the time). These men were sent to rule major provinces; Despot acquired negative connotations as the people of those provinces felt they were miss-ruled.
- Tyrant originally meant someone who came to power by gathering popular support from various factions in a Greek state. They were naturally, viewed as illegitimate by the kings and aristocrats of the time. The word acquired negative meaning because tyrants tended to resort to force to retain their power, and because of the influence of the philosophy of Plato and Aristotle.
- Dictator was a constitutional office of the Roman Republic. Because the republic's methods of making policy weren't reliably fast, there was a provision for an executive to be appointed to take care of an emergency, and his title was "dictator". The word acquired negative connotations because other forms of absolute leadership borrowed the term.
I very much doubt that the original name of the "Centrocaspian Dictatorship" had the implications of modern English "dictatorship." Given that the title must be a translation, I'm suspicious that "dictatorship" is translating some word that was meant to imply government in an emergency, and that the English translation originated with someone with an excessively classical education, who assumed everyone would apply the ancient Roman meaning.
I'm still doubtful that "dictatorship" had all of the implications of the modern English term.