We report evidence for the decays B0→D+sπ− and B0→D−sK+ and the results of a search for B0→D*+sπ− and B0→D*−sK+ in a sample of 84×106 Υ(4S) decays into BB ̄ ̄ ̄ pairs collected with the BABAR detector at the PEP-II asymmetric-energy e+e− storage ring. We measure the branching fractions B(B0→D+sπ−)=[3.2±0.9(stat)±1.0(syst)]×10−5 and B(B0→D−sK+)=[3.2±1.0(stat)±1.0(syst)]×10−5. We also set 90% C.L. limits B(B0→D*+sπ−)<4.1×10−5 and B(B0→D*−sK+)<2.5×10−5.