In this work Mossbauer spectra of CsCo_1-x-y⁵⁷Fe_xMg_yCl₃ (where x approximately 1% and y=0.07, 0.3, 0.7, 2.6%) in powdered form have been taken for a range of temperatures from 250 K down to 5.5 K. The spectra of these compounds taken below 21 K could be analysed in the same way as the spectra of CsCo_0.09Fe_0.01Cl₃ where the fits to the spectra are consistent with the magnetic phases of pure CsCoCl₃. CsCoCl₃ is a one-dimensional Ising-like antiferromagnet and moving domain walls or 'solitons' have been observed in the one-dimensionally ordered Co²⁺ chains from approximately 75 K down to 9 K. At 9 K full three-dimensional order is formed. However, experiments on Mg-doped CsCoCl₃ indicate that the Mg suppresses this transition so that it may be possible for solitons to be present below 9 K. No unequivocal evidence to indicate the presence of solitons below 9 K in Mg-doped CsCoCl₃ could be found in the Mossbauer spectra. It was found that the addition of the Mg lowers the temperature of the transition to the partially disordered phase, T_N1, from 21.1+or-0.3 K (no Mg) to 19.6+or-0.3 K (2.6 at.% Mg). The spectra of CsCoCl₃ doped with 2.6 at.% Mg showed differences that resulted in soliton relaxation rates which were approximately a factor of two higher than the rates determined for the other compounds. In all compounds the soliton relaxation rates determined above 9 K were found to be between one and two orders of magnitude below the theoretical prediction for a non-interacting soliton gas and it is suggested that this model is not appropriate for CsCoCl₃.