We propose a scheme to generate electric dipole moments in homonuclear molecular cations by creating, with an ultrashort pump pulse, a quantum superposition of vibrational states on electronic states strongly perturbed by very strong static electric fields. By field-induced molecular stabilization, the dipoles can reach values as large as 50 Debyes and oscillate on a time-scale comparable to that of the slow vibrational motion. We show that both the electric field and the pump pulse parameters can be used to control the amplitude and period of the oscillation, while preventing the molecule from ionizing or dissociating.