In this letter, the design of coded modulation for simultaneous wireless information and power transfer (SWIPT) block-fading channels is proposed, for both power-splitting (PS) and time-switching (TS) nonlinear energy harvesting (EH). With PS, although the diversity-rate tradeoff is not affected, nonlinear EH requires asymmetric modulations design which leads to an information transfer (IT) performance penalty. We thus design an asymmetric circular quadrature amplitude modulation (ACQAM) scheme that provides large performance gains compared to conventional modulations. On the other hand, we show that TS negatively impacts the diversity-rate tradeoff of the coded modulation, while an optimal QAM can be employed in the IT phase. We next derive an upper bound on the average word error rate (WER) based on a pairwise error probability analysis for both EH methods. Finally, WER simulation results are shown together with the derived bounds.