The correct answer is D) spot radiographic examination of portions of the finished weld joints. According to Coast Guard regulations, new fuel oil service piping between pumps and burners must undergo spot radiographic examination of portions of the finished weld joints, rather than a hydrostatic leak test or hydrostatic test. This requirement ensures the integrity and safety of the fuel oil piping system through non-destructive examination of the welds, which is the standard inspection method specified by the Coast Guard for this type of equipment. The other options, while potentially valid testing methods for other types of piping systems, do not align with the specific Coast Guard regulations for fuel oil service piping between pumps and burners.