Machine learning provides a promising platform for both forward modeling and the inverse design of photonic structures. Relying on a data-driven approach, machine learning is especially appealing for situations when it is not feasible to derive an analytical solution for a complex problem. There has been a great amount of recent interest in constructing machine learning models suitable for different electromagnetic problems. In this work, we adapt a region-specified design approach for the inverse design of multilayered nanoparticles. Given the high computational cost of dataset generation for electromagnetic problems, we specifically investigate the case of a small training dataset, enhanced via random region specification in an inverse convolutional neural network. The trained model is used to design nanoparticles with high absorption levels and different ratios of absorption over scattering. The central design wavelength is shifted across 350–700 nm without re-training. We discuss the implications of wavelength, particle size, and the training dataset size on the performance of the model. Our approach may find interesting applications in the design of multilayer nanoparticles for biological, chemical, and optical applications as well as the design of low-scattering absorbers and antennas.