In Warbreaker, it the history seems to be that the royal family ruled until the Manywar, and then the God Kings took over, with the events of the book taking place about 300 years and six God Kings later. The problem is that in the book, it says that there were God kings that lived for centuries. How does that fit according to the history?
To answer the question in the title: According to Hoid's story (chapter 32) there were four God Kings between the end of the Manywar and Susebron's ascension.
"And how many God Kings have there been?"
"Five, Your Majesty," the man said. "Including His Immortal Majesty, Lord Susebron, but not including Peacegiver."
"Five kings," she said. "In three hundred years?"
and then later:
"But why have there been five God Kings?" she asked. "Why did the first one die?"
"Why do any Returned pass on, Your Majesty?" Hoid asked.
“Because they are loony,” Lightsong said.
The storyteller smiled. "Because they tire. Gods are not like ordinary men. They come back for us, not for themselves, and when they can no longer endure life, they pass on. God Kings live only as long as it takes them to produce an heir."
Siri started. "That's commonly known?" she asked, then cringed slightly at the potentially suspicious comment.
"Of course it is, Your Majesty," the storyteller said. "At least, to storytellers and scholars. Each God King has passed from this world shortly after his son and heir was born. It is natural. Once the heir has arrived, the God King grows restless. Each one has sought out an opportunity to use up his Breath to benefit the realm. And then..."
He threw up a hand, snapping his fingers, throwing up a little spray of water, which puffed to mist.
"And then they pass on," he said. "Leaving their people blessed and their heir to rule."
Though later we find out that Susebron isn't a direct descendant, more the closest infant Returned at the time of the previous king's death (chapter 44).