This study addresses a problem introduced by finite-amplitude oscillations in a liquid piston thermoacoustic Stirling engine and proposes methods to overcome it. After the engine was operated by external heat, the liquid piston oscillated, keeping a flat surface when the amplitude was sufficiently low. However, it became unstable to cause ejection of droplets and formation of air bubbles because the acceleration amplitude exceeded gravitational acceleration. Two methods were proposed to recover the stable liquid surface: one method was the enlargement of the cross-sectional area of the tube around the liquid surface and the other method was the use of submerged polyethylene floats. These methods successfully suppressed the instability of the liquid piston Stirling engine and increased the pressure amplitude by almost twice of the original engine. In addition, adjusting the liquid filling level resulted in the ratio of pressure amplitude over the mean pressure reaching 18% when the acceleration amplitude was elevated to 36 m / s 2 by the installation of floats. The high-pressure amplitude is an advantage of a liquid piston thermoacoustic Stirling engine over thermoacoustic engines that use only gas as the working fluid.