Off the top of my head?

1) Assassinate the general of that army.

2) Bribe the army.

3) Move one of your own armies into one of their provinces, or park it basically right in front of that army on your own lands...sit back and wave @ the enemy and see if they'll attack.

However, what confuses me here is how you're not at war with them. If they've been on your land for multiple turns...how are you not at war?