How about parachuters?
As the OP said the Saudi military was pretty weak back then, so it would not take large forces.
Still, if they really wanted to conquer Saudi-Arabia they would need enough naval/amphibian capability to attack from the Red Sea simultaneously with the invasion of Kuwait (before the US could block them) - and they only had a collection of patrol boats etc.
If the Capital quickly falls the rest of the Country(For a country like Saudi Arabia) falls like a house of cards. For example if the Germans captured Moscow they would have won the war. If Saudi's Capital fell they would have had most of the Country under control as they would then controll all the major Oil fields.