Before finishing each turn, press the shift button to check province loyalty. Green means o.k., yellow means small chance of rebellion, red means significant chance of rebellion.

If you have the Viking Invasion expansion pack, use the autotax function. If not , you will have to micromanage taxation. Aim to make sure that each province has a loyalty of 120%. This way any accidents (vices of governors, death of king etc.) won't reduce loyalty.

Control as many sea lanes as you can. This effectively means your king is nearer to each province.

Hope this helps.