Annihilating dark matter (DM) models based on a scalar hidden sector with Higgs portal-like couplings to the Standard Model are considered as a possible explanation for recently observed cosmic ray excesses. Two versions of the model are studied, one with non-thermal DM as the origin of the boost factor and one with Sommerfeld enhancement. In the case of non-thermal DM, four hidden sector scalars which transform under a U(1)_{X} symmetry are added. The heaviest scalars decouple and later decay to DM scalars, so providing the boost factor necessary to explain the present DM annihilation rate. The mass of the annihilating scalars is limited to
24 pages, 4 figures. Expanded discussion, conclusions unchanged. Version to be published in Physical Review D