Can a country with an oligarchy as an offical form of government be successful and have prosperous citizens?
Yes, the Spartans had this and it was the most stable government in Greece for several centuries. The key point is they had a complex set of checks and balances so that no individual or subset of the hierarchy could take control from top to bottom.
So two kings with a lot of power were balanced against each other, with another four men who outranked them for many things but only served for a year, after which they were automatically put on trial and had to answer for all their decisions. Also a 30 man committee which governed nearly everything on a day to day basis.
It's as if a democratic president was automatically impeached when his term finished and had to prove his innocence. Punishments if found guilty weren't a slap on the wrist either.
There were a series of oligarchical governments in Greece after the Peloponnesian Wars, and historically they were all overthrown by popular revolt or external invasion (often encouraged or supported by rebellious elements within).
The key source of instability within an oligarchy is the restricted set of rulers. The rulers have a vested interest in both exploiting the population (in order to enrich themselves) and press them (to prevent their replacement by potentially more capable candidates). The oligarchs themselves will keep an eye on each other in order to prevent any displacement of their power, one man gathering enough power our wealth could potentially usurp the oligarchy and become a king or dictator.
There have been some systems which resemble oligarchy which do allow for prosperity and contented citizenship, however.
Ancient Greek city states were actually "Timocracies", where the vote and the right to sit on juries was only granted to property owning citizens of that polis, the idea being only propertied people would have a full interest in the mechanics of actually running the State. The US Founders had a similar idea, and the franchise was only gradually extended since the 1700's, only encompassing women, for example, in the 20th century. Since property owners are welcomed into the ruling class, it is possible (assuming the current Timocrats do not take active steps to block this) to become a property owner and enter the class, while dissolute people who become bankrupt will also lose their positions of power.
The Serenìsima Repùblica Vèneta was also oligarchic in nature, but the ability to create wealth through trade meant that the idea of a limited oligarchic class would rapidly create a conflict between the propertied rulers and propertied "outsiders". The rulers understood this risk, and over the evolution of the Serenìsima Repùblica Vèneta's Republican government, the composition of the government and ruling bodies was modified to reflect the ability to create wealth and allow participation by propertied members inside the various ruling councils of Venice. This was a combination fo Timocracy and Meritocracy, and the Veneitians were very careful to ensure that hereditary positions of power were never allowed (the Doge was always an elected position, and the few Doges who attempted to create a dynastic rule were removed from office).
So there can be systems which have the features of oligarchy, but to remain successful they need to have the ability to flexibly incorporate new membership and bring them into positions of political power.
Any form of government can be successful and have prosperous citizens. You can have benevolent dictators, wise kings and generous theocracies.
The system of government only becomes important when it all goes badly.
A despotic tyrant is very hard to remove and might require assassination or a civil war. A corrupt communist government isn't much easier nor is a king. A democracy can at least vote them out. If you can't vote them out, you're not really a democracy anymore.