We report the generation, trapping, and sympathetic cooling of individual conformers of molecular ions with the example of cis- and trans- meta-aminostyrene. Following conformationally selective photoionization, the incorporation of the conformers into a Coulomb crystal of laser-cooled calcium ions was confirmed by fluorescence imaging, mass spectrometry, and molecular dynamics simulations. We deduce the molecules to be stable in the trap environment for more than ten minutes. The present results pave the way for the spectroscopy and controlled chemistry of distinct ionic conformers in traps.