We have shown the existence of self-dual solitons in a type of generalized Chern-Simons baby Skyrme model in which the generalized function (depending only in the Skyrme field) is coupled to the sigma-model term. The consistent implementation of the Bogomol'nyi-Prasad-Sommerfield formalism requires the generalizing function becomes the superpotential defining the self-dual potential properly. Thus, we have obtained a topological energy lower bound (Bogomol'nyi bound) and the self-dual equations satisfied by the fields saturating such a bound. The Bogomol'nyi bound being proportional to the topological charge of the Skyrme field is quantized, whereas the total magnetic flux is not. As expected in a Chern-Simons model, the total magnetic flux and the total electrical charge are proportional to each other. Thus, by considering the superpotential a well-behaved function in the whole target space, we have shown the existence of three types of self-dual solutions: compacton solitons, soliton solutions decaying by following an exponential-law e-αr2 (α>0), and solitons having a power-law decay r-β (β>0). The profiles of the two last solitons can exhibit compactonlike behavior. The self-dual equations have been solved numerically, and we have depicted the soliton profiles, commenting on the main characteristics exhibited by them.