Let's split it out...
In a pitched battle:
Flying wyverns are useful, but not necessarily game changing. I'm assuming that wyverns flame breath is going to be short range, at least compared to an arrow. Wyvern wings are big and exposed. Against a prepared group of bowmen, wyverns become target practice.
You don't need any fancy weapons to kill them. A standard longbow is already designed for range and power - it could easily punch a hole through a wyvern's wing membrane. All it would take is a couple of good shots and the wyverns will fall hard.
In terms of ballista, instead of scorpions or catapults there would be a greater emphasis on 'scattershot' weapons. Wyverns are highly mobile, so you need to launch a wide area of debris in order to take them down.
There would be organised volleys of projectiles whenever the wyverns are in range, as well as dedicated anti-wyvern archers. It should be noted that wyverns are distinctly unarmored, so taking them down is not that difficult.
The best use of wyverns in that case is to give the riders bows themselves. The wyverns fly safely out of bow range, and their riders take free shots at an army below. They'd have awful accuracy, but who cares?
Of course, this assumes that the enemy is prepared. If the enemy is unprepared, the wyverns become much more useful. If the wyverns dive and the bowmen aren't ready for them, then shock and awe alone would have a huge effect.
If the battle is already won and the enemy if being routed, the wyverns become free to swoop down and inflict maximum damage. It would be the demotivating finishing blow into end a battle.
In a siege:
If sieging a castle, wyverns are a bit more useful, but they still can't replace a standard army. Wyverns still lose against bowmen, so they can't assault a fortress themselves.
But the point in siege is that the defenders can't maintain a full guard all the time. Sooner or later the defenders will slack, and then the wyverns become useful. Wyverns could very quickly lift a ladder over the walls, or drop a group of assassins in the roof, or set a stable on fire on the courtyard. It becomes much more difficult to defend against against flying foes. Wyverns would be great for constantly harassing a group of stationary defenders trapped in a castle.
In skirmishes / raids:
ThisNow, this is where the wyverns become the most useful. Wyverns move quickly, and they can terrorise an undefended populace. The wyverns can fly over the countryside, burning farms, and hurting the enemy where they're most vulnerable;vulnerable - their infrastructure.
The enemy will send groups of mounted archers to hunt the wyverns, but the flying raiders will just fly away and attack elsewhere. The wyverns have the advantage of absolute mobility, they should use that.
Sooner or later, when the people realize that their government can't protect them from these flying raiders, it'll spark riots against the government.
Of course, all this assumes that you have wyvern riders and there enemy does not. In practice, as soon as one nation tames wyverns, the other nations will work very hard to tame their own wyvern. From then ononwards, in warfare, the two opposing forces of wyvern riders will be too busy fighting each other to harass the ground.
It would be rather like the role of aircraft in World War I; the aircraft themselves are flimsy, and the air forces spend their time fighting each other, while the ground forces fightare fighting below. Sky superiority almost becomes a separate battlefield.