Trebuchet type catapults are never going to be the most accurate projectile weapons in the world but to be fair they were never really designed to be. The smallest target they would usually have to aim for was a castle. That being said there are certainly some things that you can do which will make the catapult more accurate and the shots more consistent.
Use consistent sizes, shapes and weights for ammunition. Perfectly spherical objects such as marbles create the most consistency when firing.
Get rid of any wobbles. Much of the inaccuracy is caused by the catapult wobbling as it releases. The catapult will wobble slightly different each time it is fired, so it will keep making shots land off target. Tighten any bolts and add extra bolts to improve the strength of joints. Add cross pieces to the frame to create triangles.
Tighten up the counter weight. If you have loose weights in a bag bind them together. Join the weights to the arm with a rigid rod with joints at each end rather than a rope or cable.
Lubricate the axle. This might require disassembing. Silicon lubricating spray is a pretty good, one-size-fits-all lubricant.
Make the base bigger and stand the catapult on a rubber sheet. This will dampen some of the vibration and keep the catapult more on target.
Use the smallest ring you can manage on the firing mechanism. This reduces the range of ways it can release a shot.
- Silicone spray
- Rubber sheet