Coruscant was guarded by the First Army, a powerful reserve fleet put in place during the Clone Wars. The rest of the Core Worlds surrounding the Coruscant Sector were also protected by their own sector armies, numbered two through seven, making it very difficult for enemy operatives to fly or land in the area without detection. Coruscant also had the benefit of a very big on-world security force and a large population of rich humans to support Palpatine.
I doubt that Palpatine ever really believed the First Army would turn against him. The Imperial sector armies were commanded by Grand Moffs, all of whom were pretty close confidants of the Emperor, relatively speaking. They would have been unlikely to betray him, and their subordinate officers were generally either truly loyal to the Empire or scared of defecting. In addition, it was a huge fleet; there’s no way the entire force would defect together, and a few ships wouldn’t be able to do much of anything.
I hope that helps!
~ Jacen