I don't know about Jesus necessarily being appointed King of Judea but you could probably have the Romans appoint a Davidic descendant to run Judea. Say that Herod is unable to convince Octavian that he should remain king and Octavian has him executed him for siding with Anthony in 31 BC. The Hasmoneans themselves, having previously aligned themselves with Parthia a few years earlier, are no longer trusted either. Octavian scours through Judea and after a few months, decides for a third and decisive choice: Joseph, an elderly lowly carpenter from an obscure Galilean village named Nazareth yet descended from King David...
How Romans even could be sure that someone is descendant of king David? There is not way know that surely and they hardly just take seriously some family legends. And wouldn't Romans just make Judea normal province instead kingdom annexed by Rome? They didn't appoint new pharaoh after Cleopatra VII so I don't believe that they would appoint new king to Judea.