The idea of Corinthia as a loose collection of city states is the pastiche idea, IMHO. Roy Thomas wrote the comics in that fashion.
To write Corinthia, I presumed "Rogues in the House" took place there. Here are some lines in Howard's "Rogues in the House":
"Murilo's voice sank to a whisper. 'Nabonidus, the king's priest!'"
"Nabonidus would strike through the king - of that he was certain."
"'You exploit a whole kingdom for your personal greed, and under the guise of disinterested statesmanship, you swindle king, beggar, the rich, oppress the poor, and sacrifice the whole future of the nation for your ruthless ambition."
"I had intended telling the king a jest about you in the morning."
"Then the king is unaware of my foreign enterprises."
etc.
On the other hand, Howard says in a letter that he sees
Rogues in the House taking place in a city-state west of Zamora, which could mean Corinthia, or it could be a little semi-nation between Zamora, Brythunia, and/or Corinthia. In this case, we have virtually no stories taking place in Corinthia.
There also appears a group of "nationalists," which appears to be a political faction of some sort, so the king may not be the sole power.
In "The Hour of the Dragon," Howard says:
'The older kingdoms of Ophir, Corinthia, and western Koth, which had been subject to the kings of Acheron, regained their independence with the fall of the empire.'
Howard calls Corinithia a kingdom, which implies a king, so I went with that, and created the senate based on pastiche novels, which allowed the existance of both a king and city-states.
Here is the original paragraph discussing this from RoK:
Road of Kings said:
Rogues in the House mentions a king; however, Howard does not name the city. Does Corinthia have a single king, or is it a collection of city-states, each with a king? Comments by Howard show that it is a city state, yet the king commands imperial legions, again implying the existence of a single ruler over all Corinthia. Opposing political factions are rampant in the city. Conan the Fearless, by Steve Perry, indicates the existence of senators, which supports the political factions indicated by Howard. Conan the Great, by Leonard Carpenter, mentions a governing council. Corinthians, then, are ruled by bodies of politicians and a king reigns supreme over that senatorial council.