Diocletian and the Tetrarchy
Around 280 AD, the Sassanids gradually stopped attacking the Roman Empire so much. They were having civil wars of their own, and the Huns were attacking them from the north. Because the Romans didn't have to fight in the East so much, they were able to concentrate on the Germans in the North, and managed to push them back for a while. They were also able to end the revolts inside the Empire.
The Romans were helped in this project by having a young, energetic, and very skilled Emperor named Diocletian. Diocletian came to power in 284 AD. Like other Emperors of this time, he was an army general. Diocletian first pushed back the Sassanids and the Germans. Then he ended the revolts. Then he tried to solve the problem of the civil wars between the two halves of the army. Diocletian worked out a system where there would always be two Emperors, and each of these Emperors would have two assistants. This system is called the Tetrarchy (rule of four). When one of the Emperors died, his assistant would move up to being Emperor, and choose a new assistant.
The four Tetrarchs
The four tetrarchs - aren't they cute?
Because Diocletian believed that only patriotic unity (everybody working together) would save the Empire, he was against anybody who seemed to be different from most Romans, or different from himself. This led Diocletian to try to force people not to follow the Manichaean religion anymore. Most Manichaeans either abandoned their faith or fled to the Sassanid Empire. Then Diocletian tried to force people not to be Christians anymore. This time it didn't work as well - there were more Christians, and they didn't want to move out of the Empire.
To find out more about Diocletian and Constantine and their successors, check out these books from Amazon.com or from your library:
The Roman Empire, by Don Nardo (1994). For middle schoolers and high schoolers - from Augustus to the fall of Rome.
Diocletian and the Roman Recovery, by Stephen Williams (1985). Gives Diocletian more credit for the recovery than I would, but there aren't any other biographies of Diocletian in English.
Constantine, by Nancy Zinsser Walworth (1989). A biography for kids.
Constantine and the Conversion of Europe, by A. H. M. Jones (1948, reprinted 1979). Still the best account of how Constantine came to convert to Christianity, and of his relationship with the Church throughout his reign. It's not specifically for kids, but high schoolers could read it.
The Life and Times of Constantine the Great: The First Christian Emperor, by D. G. Kousoulas (2nd edition 2003). A biography of Constantine.
Julian the Apostate, by G. W. Bowersock (1978). A great biography, and lively reading too!