The formation of stable ground and excited states of carbon-like negative ions Ge^- and Sn^- in low-energy electron-atom scattering as Regge resonances is investigated. The recently developed Regge-pole methodology is used for the calculations together with the Thomas-Fermi type potential which incorporates the vital core polarization interaction. The extracted binding energies (BEs) for the ground and the excited states of the Ge^- and Sn^- negative ions are found to agree excellently with the measured values. The Ramsauer-Townsend (RT) minima, the shape resonances and the Wigner threshold law are also determined.