We propose a scheme for exciting steady-state tunneling oscillations of an electronic wave packet in a semiconductor coupled quantum-well structure with strain of the opposite polarity in the two wells, A detailed study of the four-wave mixing process in this structure is then presented, based on the density matrix formalism, Our results show that a resonance peak is introduced in the four-wave mixing frequency response at the tunneling frequency, leading to a significant enhancement in the wavelength conversion efficiency for low temperature operation, Furthermore, we consider this structure under the same excitation condition as a potential source of coherent radiation in the terahertz frequency band.