Carbon dioxide (CO2) and methane (CH4) are the primary greenhouse gases (GHGs) that drive global climate change. CO2 reforming of CH4 or dry reforming of CH4 (DRM) is used for the simultaneous conversion of CO2 and CH4 into syngas and higher hydrocarbons. In this study, DRM was investigated using Ag–Ni/Al2O3 packing and Sn–Ni/Al2O3 packing in a parallel plate dielectric barrier discharge (DBD) reactor. The performance of the DBD reactor was significantly enhanced when applying Ag–Ni/Al2O3 and Sn–Ni/Al2O3 due to the relatively high electrical conductivity of Ag and Sn as well as their anti-coke performances. Using Ag–Ni/Al2O3 consisting of 1.5 wt% Ag and 5 wt% Ni/Al2O3 as the catalyst in the DBD reactor, 19% CH4 conversion, 21% CO2 conversion, 60% H2 selectivity, 81% CO selectivity, energy efficiency of 7.9% and 0.74% (by mole) coke formation were achieved. In addition, using Sn–Ni/Al2O3, consisting of 0.5 wt% Sn and 5 wt% Ni/Al2O3, 15% CH4 conversion, 19% CO2 conversion, 64% H2 selectivity, 70% CO selectivity, energy efficiency of 6.0%, and 2.1% (by mole) coke formation were achieved. Sn enhanced the reactant conversions and energy efficiency, and resulted in a reduction in coke formation; these results are comparable to that achieved when using the noble metal Ag. The decrease in the formation of coke could be correlated to the increase in the CO selectivity of the catalyst. Good dispersion of the secondary metals on Ni was found to be an important factor for the observed increases in the catalyst surface area and catalytic activities. Furthermore, the stability of the catalytic reactions was investigated for 1800 min over the 0.5 wt% Ag-5 wt% Ni/Al2O3 and 0.5 wt% Sn-5 wt% Ni/Al2O3 catalysts. The results showed an increase in the reactant conversions with an increase in the reaction time.