We demonstrate a compact solid-state laser source for high-resolution two-photon spectroscopy of the 1S-2S transition in atomic hydrogen. The source emits up to 20 mW at 243 nm and consists of a 972 nm diode laser, a tapered amplifier, and two doubling stages. The diode laser is actively stabilized to a high-finesse cavity. We compare the new source to the stable 486 nm dye laser used in previous experiments and record 1S-2S spectra using both systems. With the solid-state laser system, we demonstrate a resolution of the hydrogen spectrometer of 6×10^11, which is promising for a number of high-precision measurements in hydrogenlike systems.