Quantum memories for light are essential components in quantum technologies like long-distance quantum communication and distributed quantum computing. Recent studies have shown that long optical and spin coherence lifetimes can be observed in rare earth doped nanoparticles, opening exciting possibilities over bulk materials e.g. for enhancing coupling to light and other quantum systems, and material design. Here, we report on coherent light storage in Eu$^{3+}$:Y$_2$O$_3$ nanoparticles using the Stark Echo Modulation Memory (SEMM) quantum protocol. We first measure a nearly constant Stark coefficient of 50 kHz/(V/cm) across a bandwidth of 15 GHz, which is promising for broadband operation. Storage of light using SEMM is then demonstrated for times up to 40 $mu$s. Pulses with two different frequencies are also stored, confirming frequency-multiplexing capability, and are used to demonstrate the memory high phase fidelity.