Previously, I tried hooking up a "rapid pulser" to some dispensers, but it failed miserably (never lasted for more than 2 or 3 seconds) so I decided to try out a 1 tick "repeater clock"hooked up to the pistons. However, this design needs to have a one tick pulse "injected" into the circuit first. Is there a way to create a circuit/device that outputs power for one tick only?
What you actually want is a clock circuit. The simplest is a repeater, a block of any kind, three pieces of redstone, and one redstone torch, arranged like so:
The torch should be attached to the side of the block, and the repeater powering into the adjacent side of the block and (to avoid burning out the torch) set to 2 ticks or more.
This will give you a stable clock signal that you can pull from almost any part of the circuit. You can easily add an on/off switch on top of the block to stop and restart the cycle.