[Aroki]

My guess is that you're having one (or more) of these problems
1. The backstroke of the piston is catching on the frisbee above, causing it to not load right
2. The bucket is slightly to big allowing the frisbees to load incorrectly
3. The slot cut for the frisbee to leave the bucket is to small

If you have time, switching from a piston to a motor with a cam-shaped arm would probably best fix you problems. For our one we used a KOP window motor with the plastic hub for it, and attached a 1/4in thick plexiglass cam-shaped arm. Having a motor and cam allows for some degree of error (the circular motion and rounded shape of the arm let it roll if it isn't lined up perfectly right instead of driving it into the wall.)

If you are short on time, I'd keep the piston but make the head that strikes the disc thinner and is smooth on the top so it doesn't hit the second frisbee (not sure if this is your problem). Also if you had a U-shaped head so the piston aligned the frisbee when it fired. You'll also want to make your piston fire relatively slowly, so the head has time to align it. Also if your design allows it, increasing the exit slot for the frisbee may help.

Either way checking to make sure your bucket stacks the discs nicely will probably make the biggest difference, a slight funnel (like a 1/2in from the top diameter to the bottom diameter) can help with this.

*Please note that much of the above advice (especially regarding the piston) is untested speculation on my part, and may be completely wrong. Also it's 12:30am my time and I'm sick so I'm probably not thinking clearly