Locally resonant metamaterials are an active field of research for wave phenomena in fields as diverse as electromagnetics, acoustics, and dynamics. A typical application is wave attenuation in a frequency range called a band gap. Many implementations have been reported, often based on models of idealized mass-spring resonators or simple beams. Introducing them into industrial applications is however not straightforward. Resonating beams become exceedingly large for low-frequency band gaps, which are confined to a narrow frequency region so that they are no good solution for wideband vibration issues. We present a method to design multi-band gap metamaterials, using compact, multimodal mechanical resonators. Therefore, a resonator should yield a set of prescribed modal frequencies and modal masses. For complex geometries, there is no analytical formula to predict the first eigenmodes which are typically calculated using finite element simulations. The inverse problem, finding a suitable geometry that yields a desired property, is called topology optimization. We propose an intuitive way to apply machine learning to the inverse design of realizable resonators. A family of helicoidal geometries, representing a coiled-up vibrating beam, is described by 6 geometrical parameters. A set of 10000 designs is simulated using finite elements to retrieve their first 12 eigenfrequencies and modal masses. This data set, mapping a 1 × 6 input vector to a 2 × 12 output matrix (or a subset thereof), is used to train a convolutional auto-encoder (cVAE). The encoder maps the input geometry vector to the dynamic response matrix. The decoder maps the dynamic response back to a geometric design. By adding a latent space in the middle layer, thousands of geometries can be generated within seconds. This approach is used to design resonators with two prescribed eigenmodes. We compare the cVAE prediction to finite element calculations, and validate the approach by experimental examples.