A two-stage gas-coupled Stirling/pulse tube refrigerator (SPR), whose first and second stages respectively involve Stirling and pulse tube refrigeration cycles, is a very promising spaceborne refrigerator. The SPR has many advantages, such as a compact structure, high reliability, and high performance, and is expected to become an essential refrigerator for space applications. In research regarding gas-coupled regenerative refrigerator, the energy flow distribution between the two stages, and optimal phase difference between the pressure wave and volume flow, are two critical parameters that could widely influence refrigerator performance. The effects of displacer displacement on the pressure wave, phase difference, acoustic power distribution, and inter-stage cooling capacity shift of the SPR have been investigated experimentally. Notably, to obtain the maximum first-stage cooling capacity, an inflection point in displacement exists. When the displacer displacement is larger than the inflection point, the cooling capacity could be distributed between the first and second stages. In the present study, an SPR was designed and manufactured to work between the liquid hydrogen and liquid oxygen temperatures, which can be used to cool small-scale zero boil-off systems and space detectors. Under appropriate displacer displacement, the SPR can reach a no-load cooling temperature of 15.4 K and obtain 2.6 W cooling capacity at 70 K plus 0.1 W cooling capacity at 20 K with 160 W compressor input electric power.