Catapults are great for one thing and one thing only: training siege operators.
Build a 3x6 tunnel that looks like this:
CCC._|
CCC._|
CCC._|
Where C is the catapult, _ is a channeled-out line (do NOT remove the ramps below it, you want your dwarf to be able to go down and back up) and | is a wall, whether constructed or natural.
Set the catapult facing the wall, then set it on "fire at will". Your trainee siege operator will start firing rocks at the wall, which will then drop into the channeled moat. Since siege ammo falling down a Z-level or more is not destroyed, the rock will sit on the ground ready to be retrieved. Since it is now the closest rock to the catapult, the operator will go fetch it rather than go traipsing across the fortress looking for another rock. (Actually, due to some uninteresting details, he'll go fetch another rock ONCE, then cycle between two rocks in his training). Result: a siege operator who's spending ALL his time training his skill, and who'll hit Legendary in just a couple seasons. Then you can assign him to the fortress-defense ballistas.
For extra training time, use the square in front of the catapult for two 1x1 stockpiles (of food and booze, respectively) and build a bed on the third square. Then build a burrow around your catapult training hall and restrict your trainee to the burrow. Now he won't even have to go away for booze/food breaks!