Inelastic neutron scattering studies in single crystals of TbInO3 and TbIn0.95Mn0.05O3 with nearly triangular antiferromagnetic lattice are reported. At low energies, a broad and apparently gapless continuum of magnetic excitations, located at the triangular lattice (TL) Brillouin zone boundary, is observed. The data are well described by the uncorrelated nearest-neighbor valence bonds model. At higher energies, a broad excitation branch dispersing from the TL zone boundary is observed. No signs of static magnetic order are found down to the temperatures two orders of magnitude smaller than the effective interaction energy. The fluctuating magnetic moment exceeds two-thirds of the Tb3+ free-ion value and is confined to the TL plane. These observations are consistent with a TL-based spin liquid state in TbInO3.