Biological ion channels are able to generate coherent and oscillatory signals from intrinsically noisy and stochastic components for ultrasensitive discrimination with the use of stochastic resonance, a concept not yet demonstrated in human-made analogs. We show that a single-walled carbon nanotube demonstrates oscillations in electroosmotic current through its interior at specific ranges of electric field that are the signatures of coherence resonance. Stochastic pore blocking is observed when individual cations partition into the nanotube obstructing an otherwise stable proton current. The observed oscillations occur because of coupling between pore blocking and a proton-diffusion limitation at the pore mouth. The result illustrates how simple ionic transport can generate coherent waveforms within an inherently noisy environment and points to new types of nanoreactors, sensors, and nanofluidic channels based on this platform.