The shear wave dispersion magneto-motive ultrasound (SDMMUS) method was recently developed to analyze the mechanical properties of a viscoelastic medium. This technique is based on the interaction of magnetic nanoparticles (MNPs) with an external magnetic field to generate a shear wave within the medium labeled with MNPs. The propagation of this wave provides information about the viscoelastic properties of the medium. In a previous work by Arsalani et al (2018), magnetite NPs were synthesized by a co-precipitation method and coated with natural rubber latex (NRL). In order to investigate the effect of NRL on the size and magnetization of MNPs, varying amounts of NRL (zero, 100 µl, and 800 µl of a stock solution of NRL) were used during the synthesis process. The results showed that MNPs prepared with 800 µl of NRL, named as MNPs-800NRL, had the smallest size and highest magnetization. In the present paper, the main objective is to investigate whether MNPs-800NRL, having the highest magnetization, is also the best option for SDMMUS experiments among others. All experiments were performed using gelatin tissue-mimicking phantoms labeled with the aforementioned MNPs. The two factors of core size and magnetization were considered, and based on the observed results, the effect of magnetization was more prominent than that of the core size on the induced displacements. MNPs coated with a thicker NRL shell, having the highest magnetization value, enhanced the sensitivity and the signal to noise ratio in SDMMUS. Various concentrations of these optimized MNPs were also examined, to investigate the lowest possible concentration for observing shear waves in the SDMMUS technique.