The current dataset is composed of damped solitons of the Schrödinger equation in periodic nonlinear oscillator chains under external excitation within the stability region. Unlike resonators subjected to parametric excitation, chains exclusively subjected to external excitation do not have known analytical solutions for Intrinsic Localized Modes (ILMs) when damping is considered. The results consist of nonlinear damped periodic structures that effectively describe the behavior of solitonic solutions using the continuous analog of Newton's method.