So I've been reading Tacitus and Gibbon recently, as well as listening to Mike Duncan's History of Rome podcast religiously, and thinking a lot about why the Roman Empire fell. I want to write a Rome-wank, but I know that scenario has been beaten to death, and there's scarcely an original take on it beyond "Julius Caesar lives a little longer" or "Hadrian doesn't abandon Trajan's conquests", neither of which are particularly realistic and both of which miss the main point. The Roman Empire, as it was conceived by Augustus (and later by Diocletian) definitely could not have survived much longer than it did IOTL for a lot of reasons, but the chief among them is this: the institutional weakness of the Roman system.
The primary institutional weakness was the same weakness that plagues all absolute monarchies. The emperor was all-powerful, so rogue generals had nothing to lose and everything to gain by rebelling and replacing the emperor, and this problem plagued the Romans from Sulla's first march on Rome to the fall of Romulus Augustulus. The only solution to this that I can see would be the creation of another institution to balance out the power of the emperor (i.e. like how the British gradually developed the Magna Carta and eventually the parliament, and much later the institutions of the government displaced the power of the crown). However, this process would be a centuries-long undertaking, and I'm just looking for a POD to get that process up and running.
One's natural instinct is to say that there's already another institution that can balance the emperors: the senate. But I doubt very severely that they could serve that purpose. The senate ran the Republic for 500 years and proved time and time again that they were too corrupt and petty to form an effective governing body. They were too inbred and localized and far too wrapped up with the concerns of the city of Rome and Italy itself to serve as an effective governing body for a diverse and multinational empire.
My preliminary decision for the POD is to have Tiberius die in 9 BCE instead of Drusus, leaving Drusus (a less paranoid and more mentally stable leader) in line for the throne, making the ascension of Germanicus more possible (IOTL he may have been poisoned under Tiberius' orders). Between Drusus and Germanicus, it's likely that one of them would rule for long enough and have the foresight to establish a "provincial senate" of sorts drawn from the elites from all corners of the empire and give that body the right to elect the princeps perhaps. This might serve as a good foundation for a long-term institutional stability in the Roman Empire.