In several low-field Nuclear Magnetic Resonance (LF-NMR) and surface nuclear magnetic resonance applications, i.e., in the frequency range of kHz, high sensitivity magnetic field detectors are needed. Usually, low-Tc superconducting quantum interference devices (SQUIDs) with a high field sensitivity of about 1 fT/Hz(1/2) are employed as detectors. Considering the flux trapping and operational difficulties associated with low-Tc SQUIDs, we designed and fabricated liquid-nitrogen-cooled Cu coils for NMR detection in the kHz range. A cooled coil system consisting of a 9-cm diameter Cu coil and a low noise preamplifier was systematically investigated and reached a sensitivity of 2 fT/Hz(1/2) at 77 K, which is 3 times better compared to the sensitivity at 300 K. A Q-switch circuit as an essential element for damping the ringing effects of the pickup coil was developed to acquire free induction decay signals of a water sample with minimum loss of signal. Our studies demonstrate that cooled Cu coils, if designed properly, can provide a comparable sensitivity to low-Tc SQUIDs.