Velasco has a good job at doing it in After Actium as he said. But although I know people are going to come on here citing Peter Heather for the first century, I think its feasible then (though definitely the social and political aspects of 2nd century Germania are more ready for Roman occupation).
Basically, if you want it in the First century, two things must not happen (one is optional though). First and foremost, you cannot have the Great Illyrian Revolt spring up. That drained all of Rome's manpower (Augustus had to recruit slaves into the army) to put down, and incidentally, Ariminius was in Illyria at the time and went to Germania thinking that was the best time to try to get a revolt going, while ROme was distracted. It also diverted many legions Tiberius was controlling in Germania and planning to use for an invasion of Marcomannia, and Tiberius himself, to Illyria. This meant Varrus was put in control of a vastly reduced force, and you know what happens from there.
A second optional thing would be to have Drusus not only live longer, but be the successor to Augustus. This is fairly easy-Tiberius was only recalled from his self-imposed exile on Rhodes because Augustus' two grandsons had died and Agrippa Posthumus would not suitable for succession-meaning he was the last option for Augustus. If Drusus is still alive, Tiberius isn't recalled and Drusus gets the succession. This also means he's still in Germania doing his fantastic job, and since the Great Illyrian revolt hasn't happened likely participates in the invasion of Marcomannia.
Now since Drusus is emperor, he's not going to abandon the province he worked so hard to conquer-think of it as a pride factor-and his son and successor Germanicus would also likely be doing heavy campaigning in the area as well-it is unlikely he would give it up willy nilly either-it would take a Teutoberg like disaster to make Rome consider withdrawing again.
Now, by the time of Germanicus' death, Germania has been under Roman control for more or less 40-60 years. More than enough time for it to be, if not Romanized, incorporated into the Imperial fold for the long haul. The Romans were already building cities in Germania at least between the Rhine and the Wesser, and this would continue. They were also cuddling up to the local elites and showing them the benefits of Roman rule-as long as they are governed fairly and under competent administration, the Germanian's shouldn't pose much of a problem to keep under control.
As Velasco did in his TL, it would be of great help for the Romans to do some canal projects to improve communication and supply lines. Most important would be a Rhine-Rhone canal.
Hope this helped!