The protonated acetylene cation, C2H3+, (also known as the vinyl cation) and the proton-bound acetylene dimer cation (C4H5+) are produced by a pulsed supersonic nozzle/pulsed electrical discharge cluster source. The parent ions are also generated with weakly attached argon "tag" atoms, e.g., C2H3+Ar and C4H5+Ar. These ions are mass selected in a specially designed reflectron time-of-flight mass spectrometer and studied with infrared laser photodissociation spectroscopy in the 800-3600 cm(-1) region. Vibrational resonances are detected for both ions in the C-H stretching region. C2H3+ has a strong vibrational resonance near 2200 cm(-1) assigned to the bridged proton stretch of the nonclassical ion, while C4H5+ has no such free-proton vibration. Instead, C4H5+ has resonances near 1300 cm(-1), consistent with a symmetrically shared proton in a di-bridged structure. Although the shared proton structure is not the lowest energy isomer of C4H5+, this species is apparently stabilized under the supersonic beam conditions. Larger clusters containing additional acetylene units are also investigated via the elimination of acetylene. These species have new IR bands indicating that rearrangement reactions have taken place to produce core C4H5+ ions with the methyl cyclopropane cation structure and/or the protonated cyclobutadiene isomer. Ab initio (MP2) calculations provide structures and predicted spectra consistent with all of these experiments.