The removal of sulfur from petroleum products is an important step in the refining process. Several techniques have been developed to address the limitations of hydrodesulfurization, including adsorptive desulfurization. One of the requirements of the adsorptive desulfurization process is the use of efficient and cost-effective materials. In this work, activated carbon (AC) derived from waste rubber tires was loaded with cobalt and copper nanoparticles. The prepared materials were evaluated for their efficiency in batch and fixed-bed systems for the simultaneous adsorptive desulfurization of thiophene (T), benzothiophene (BT), dibenzothiophene (DBT), 5-methyl-1-benzothiophene (MBT), 4-methyldibenzothiophene (MDBT), and 4,6-dimethyldibenzothiophene (DMDBT). AC loaded with cobalt and copper (CoCu/AC) showed enhanced simultaneous adsorptive desulfurization of the sulfur compounds in the order of DBT > MDBT > DMDBT > MBT > BT > T. The adsorption experimental data showed the closest match with the pseudo-second-order kinetic. The intraparticle diffusion indicates that other mechanisms may be included in the adsorption process along with the intraparticle diffusion. Simultaneous adsorptive desulfurization in fixed bed models indicated the following trend in breakthroughs: DBT > MDBT > DMDBT > MBT > BT > T. A mechanism proposed via the π-complexation and the direct S-M interaction could justify the trend in adsorption capacity.