Saudi Arabia is a stable country as exemplified by the lack of war, the strong economy and diplomatic relations. Saudi Arabia is a wealthy economy spread throughout the country which provides stability in that the likelihood of any uprisings are diminished with economic satisfaction. Saudi Arabia maintains diplomatic relations with many EU countries, as well as, Middle East and the West.
No, I do not think Saudi Arabia is stable. When you have a country with an over abundance of a fossil fuel, and that over abundance is strictly in the hands of a wealthy elite few, there is extreme wealth at the top, but there is no real stability. The country has people starving in outlying areas, religious conflicts, internal strife and a constant threat of war.
No, Saudi Arabia is not stable, because there is a lot of terrorism in that nation. In fact, that is where most of the September 11 terrorists came from. Underneath the surface there are some deep-seeded extremist groups in the country, even though on their face they appear to be rich because of oil.
Saudi Arab is one of the biggest influence in the stability of the Middle East and Persian Gulf area. However they have a lot of internal problems with the country. Human rights issues and equality are always a challenge and cause protests and disgruntled citizens. In addition, several terrorist cells are also still alive within the country.