Oscillations in the formation and dissolution of molecular assemblies inside living cells are pivotal in orchestrating various cellular functions and processes. However, designing such rhythmic patterns in synthetic cells remains a challenge. Here, we demonstrate the spontaneous emergence of spatio-temporal oscillations in the number of droplets, size, and their spatial distribution within a synthetic cell. The coacervate-based droplets in these synthetic cells sediment and fuse at the cell's bottom. Through a size control mechanism, the sedimented, large droplets shrink by expelling droplet material. The expelled molecules nucleate new droplets at the top of the synthetic cell, which grow and sediment again. These oscillations are sustained by converting chemical fuel into waste and can continue for hundreds of periods without evidence of fatigue. Strikingly, the period of the oscillation is in the minute's regime and tunable. The design of oscillating artificial organelles in synthetic cells brings us closer to creating more life-like materials and de novo life.