In this study, pyrazole tartrate (Pya·DL) and tartaric acid (DL) complexed with cobalt–iron bimetallic modified hydrogen-type mordenite (HMOR) were prepared using the ion exchange method. The results demonstrate that the stability of the dimethyl ether (DME) carbonylation reaction to methyl acetate (MA) was significantly improved after the introduction of Pya·DL to HMOR. The Co∙Fe∙DL-Pya·DL-HMOR (0.8) sample exhibited sustainable stability within 400 h DME carbonylation, exhibiting a DME conversion rate of about 70% and MA selectivity of above 99%. Through modification with the DL-complexed cobalt–iron bimetal, the dispersion of cobalt–iron was greatly enhanced, leading to the formation of new metal Lewis acidic sites (LAS) and thus a significant improvement in catalysis activity. Pya·DL effectively eliminated non-framework aluminum in HMOR, enlarged its pore size, and created channels for carbon deposition diffusion, thereby preventing carbon accumulation and pore blockage. Additionally, Pya·DL shielded the Bronsted acid sites (BAS) in the 12 MR channel, effectively suppressing the side reactions of carbon deposition and reducing the formation of hard carbon deposits. These improvements collectively contribute to the enhanced stability of the DME carbonylation reaction.