Motivated by the protein structure prediction problem, we develop two variants of the Hamiltonian replica exchange methods (REMs) for efficient configuration sampling, (1) the scaled hydrophobicity REM and (2) the phantom chain REM, and compare their performance with the ordinary REM. We first point out that the ordinary REM has a shortage for the application to large systems such as biomolecules and that the Hamiltonian REM, an alternative formulation of the REM, can give a remedy for it. We then propose two examples of the Hamiltonian REM that are suitable for a coarse-grained protein model. (1) The scaled hydrophobicity REM prepares replicas that are characterized by various strengths of hydrophobic interaction. The strongest interaction that mimics aqueous solution environment makes proteins folding, while weakened hydrophobicity unfolds proteins as in organic solvent. Exchange between these environments enables proteins to escape from misfolded traps and accelerate conformational search. This resembles the roles of molecular chaperone that assist proteins to fold in vivo. (2) The phantom chain REM uses replicas that allow various degrees of atomic overlaps. By allowing atomic overlap in some of replicas, the peptide chain can cross over itself, which can accelerate conformation sampling. Using a coarse-gained model we developed, we compute equilibrium probability distributions for poly-alanine 16-mer and for a small protein by these REMs and compare the accuracy of the results. We see that the scaled hydrophobicity REM is the most efficient method among the three REMs studied.