The major reason for the lack of serious international conflicts in the 1920s was World War I.
When thinking about this time, we must first remember that there were many fewer possible conflicts in those days. Essentially all of Africa and the Middle East was controlled by one European country or another, making it so that there could not be conflicts between (for example) Iran and Iraq.
This means that major conflicts in the world had to include a major European power, the United States, or possibly Japan. All of these countries were too affected by WWI to engage in major conflicts. The European countries, of course, had been directly affected. Russia had become the Soviet Union and was largely concerned with internal affairs. Germany was dismembered and weakened. France and England had been devastated by WWI and wanted no part of another conflict. The United States was beginning to pull away from international involvement. Japan was much less affected by the war but was not yet disillusioned enough with the international order to want to change it.
Therefore, the major reason for the lack of conflict during the 1920s was the fact that a tremendous conflict had just occurred and no major power had the strength and/or the desire to start another one at that point.