General Fusion is building the Fusion Demonstration Plant to demonstrate a magnetized target fusion scheme in which a deuterium plasma is heated from 200 eV to 10 keV by piston-driven compression of a liquid-lithium liner. The multilayer coaxial time-of-flight neutron emission spectrometer is designed to measure the ion temperature near peak compression at which time the neutron yield will approach 1018 neutrons/s. The neutron energy distribution is expected to be Gaussian since the machine uses no neutral beam or radio-frequency heating. In this case, analysis shows that as few as 500 coincidence events should be sufficient to accurately measure the ion temperature. This enables a fast time resolution of 10 µs, which is required to track the rapid change in temperature approaching peak compression. We overcome the challenges of neutron pile-up and event ambiguity with a compact design having two layers of segmented scintillators. The error in the ion temperature measurement is computed as a function of the neutron spectrometer's geometric parameters and used to optimize the design for the case of reaching 10 keV at peak compression.