We show that three SU(2) singlet neutral scalars (two CP-even and one CP-odd) in the spectrum of models based on the gauge symmetry SU(3)_c X SU(3)_L X U(1)_X, which do not contain exotic electric charges, are realistic candidates for thermally generated self-interacting dark matter in the Universe, a type of dark matter that has been recently proposed in order to overcome some difficulties of collisionless cold dark matter models at the galactic scale. These candidates arise without introducing a new mass scale in the model and/or without the need for a discrete symmetry to stabilize them, but at the expense of tuning several combinations of parameters of the scalar potential.