We present experiments and theory of a constant flow-driven microfluidic oscillator with widely tunable oscillation periods. This oscillator converts two constant input-flows from a syringe pump into an alternating, periodic output-flow with oscillation periods that can be adjusted to between 0.3 s to 4.1 h by tuning an external membrane capacitor. This capacitor allows multiple adjustable periods at a given input flow-rate, thus providing great flexibility in device operation. Also, we show that a sufficiently large external capacitance, relative to the internal capacitance of the microfluidic valve itself, is a critical requirement for oscillation. These widely tunable microfluidic oscillators are envisioned to be broadly useful for the study of biological rhythms, as on-chip timing sources for microfluidic logic circuits, and other applications that require variation in timed flow switching.