Batista wouldn't have lasted much longer than 1/1/59, Castro or no:

Cuba before Castro had the third-highest per-capita income in Latin America, after Chile and Argentina. While there were great disparities in wealth between cities and the countryside, Cuba also had a thriving, educated, high-achieving middle class. They were the people who were dissatisfied enough to suppor Castro, at least initially. I think that, without Castro, the middle class would have seen Batista as standing in the way of progress and would have forced him out.

The US would have provided impetus: The Kennedy Administration, only about two years later, declared war on organized crime. The US government always called the shots in Cuba. I think the administration would have leaned on Batista to "retire" (as the US had earlier), forced the gangsters out, and would have supported some "democratically" elected leader. Cuba then might have become something like Vegas in the Seventies--still the playground (and maybe the whorehouse) of the Caribbean, but with somewhat more "respectability."