We predict and analyse a novel spin filter in semiconducting carbon nanotubes. By using local electrostatic gates, the conduction and valence bands can be modulated to form a double-barrier structure. The confined region below the valence band defines a Zener quantum dot, which exhibits resonant tunnelling. The resonances split in a magnetic field to make a bipolar spin filter for applications in spintronics and quantum information processing. We model this using envelope function theory and show that this is in excellent agreement with a corresponding tight-binding calculation.