We propose a framework for inducing strong optomechanical effects in a suspended carbon nanotube based on deformation potential (DP) 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 and a characteristic size in the 10nm range. A transverse field induces a tunable parametric coupling between the quantum dot and the flexural modes of the nanotube mediated by electron–phonon interactions. We derive the corresponding excitonic DPs and show that this interaction enables efficient optical ground-state cooling of the fundamental mode and could allow us to realize the strong and ultra-strong coupling regimes of the Jaynes–Cummings and Rabi models.