<p>Seismic metamaterials (SMs) have attracted considerable attention for their ability to mitigate low-frequency vibrations induced by earthquakes and traffic. While stiffness influences the resonant frequency, achieving stiffness tuning for customized Rayleigh wave bandgaps (RWBs) remains a significant challenge. Here, we propose a stiffness-tunable SM consisting of periodically arranged masses integrated with re-entrant structures. By adjusting the geometric parameters of the re-entrant units, the equivalent stiffness can be continuously tuned. Our analysis shows that although decreasing stiffness lowers the resonant frequency, excessive reduction causes the RWB width to shrink extremely. In contrast, tuning the stiffness to a moderate value yields a broad low-frequency RWB, with an onset frequency 16.4% lower and a relative bandwidth 13.7% larger than those of a topology-optimized design. Frequency-domain analyses further reveal surface-to-bulk wave conversion within the RWB, confirming the attenuation capability of the proposed SM. Simulations under seismic excitations show that a tailored SM reduces wave amplitudes by 42%. Moreover, an SM customized for metro-induced vibrations achieves a 65% attenuation in peak responses. By harnessing tunable stiffness in SMs, this work establishes a new design framework and structural paradigm for achieving customized RWBs, offering a promising pathway toward practical seismic protection.</p>