Keep the crown authority positive or at least at zero.
Try to avoid opinion drops as negative opinions will lead to low stability.
Try to keep wars short and effective. Long wars lead to war exhaustion which will reduce stability across your kingdom for a long time.
Rapid expansion can lead to kingdom instability. Provinces that follow a different religion/culture or are loyal to other kingdoms will always be unhappy if you take over. Make sure to gain the foreign province's loyalty before you siege the city.
Use Clerics' "Commit to Charity" skill to directly increase stability.
Make sure to destroy the rebels as soon as the spawn. Leaving rebellions unhandled can lead to them becoming famous rebels that can even hold cities across several kingdoms.
Certain Kingdom Traditions can increase stability.
