You can try to use liquid ammonia as solvent. In these conditions, cysteine or methionine should not poison the catalyst. Adding BaSO4 or BF3.Et2O in the case of methionine could also help :)
You can use glacial AcOH at room temperature. The best is monitoring by TLC if the reaction has stopped because of poisoning, and adding if needed new wet aliquots of Pd/C into the vessel.