A new data acquisition system including a Field Programmable Gate Array (FPGA) based time-resolved scaler was developed for laser-induced fluorescence and beam bunch coincidence measurements. The FPGA scaler was tested in a collinear laser-spectroscopy experiment on radioactive (37)K at the BEam COoler and LAser spectroscopy (BECOLA) facility at the National Superconducting Cyclotron Laboratory at Michigan State University. A 1.29 μs bunch width from the buncher and a bunch repetition rate of 2.5 Hz led to a background suppression factor of 3.1 × 10(5) in resonant photon detection measurements. The hyperfine structure of (37)K and its isotope shift relative to the stable (39)K were determined using 5 × 10(4) s(-1) (37)K ions injected into the BECOLA beam line. The obtained hyperfine coupling constants A((2)S(1/2)) = 120.3(1.4) MHz, A((2)P(1/2)) = 15.2(1.1) MHz, and A((2)P(3/2)) = 1.4(8) MHz, and the isotope shift δν(39, 37) = -264(3) MHz are consistent with the previously determined values, where available.