An oscillating two-stream instability (OTSI) is investigated in plasma, which has hot and cold positive ions, negative ions, and the electrons. For this, a long wavelength plasma wave is considered to be driven by two copropagating lasers with frequencies ωL1 and ωL2, such that their difference is almost equal to the electron plasma frequency ωp. In the present mechanism, this plasma beat wave (ωb, kb) is taken to grow in amplitude, so that it becomes susceptible to the OTSI and produces a low frequency electrostatic mode (ω, k), and two shorter wavelength Langmuir wave sidebands (ω1, k1) and (ω2, k2) with ω1 = ω − ωb, ω2 = ω + ωb, k1 = k − kb, and k2 = k + kb in the plasma. The effects of charge number Z, mass, temperature, and density of the ions are studied on the growth rate of the instability, and the amplitudes and phases of the sideband waves generated during the OTSI. It is found that the effects of charge number and mass of the ions are significant on the instability.