In this work, the second harmonic generation from excitonic transitions in semiconductor quantum dots is computationally studied. By integrating a density matrix treatment with a partial configuration interaction approach, we obtain the second order susceptibility as a function of externally applied electric and magnetic fields for highly confined neutral and charged excitons. Our results show an enhancement in the nonlinear response with respect to analogous optical processes based on intraband transitions, and predict their efficient tunability by taking advantage of the interplay between Coulomb effects and field-driven wave function manipulation.