We analyze a framework for optical manipulation of the motional state of a suspended carbon nanotube based on deformation potential exciton-phonon coupling. The excitons are confined using an inhomogeneous axial electric field which generates optically active quantum dots with a level spacing in the milli-electronvolt range. A transverse field induces a tunable parametric coupling between the quantum dot and the flexural modes of the nanotube. We show that this interaction enables efficient optical ground-state cooling of the fundamental mode and will allow access to quantum signatures in its motion.