I once built a "coil gun" with little power, but it worked. It was mainly meant as a demonstration device for a larger project (which I never got around to building).
What I did was take some wire (telephone hookup wire, 14-16 ga, I think), and wrapped six coils onto a length of rigid plastic tubing (about half the diameter of a plastic soda straw, but with thicker walls so it didn't bend); each coil had about 50 turns of wire. I connected one end of each coil together (common), and the other ends I ran to brass tacks on a board. I hooked the common end to the negative terminal of a 12 volt wall-wart (1-2 amp). The positive end of the wall-wart I ran to another wire with a bare end. I cut a small finishing nail such that it would fit inside the tube. With it in place, then rapidly sliding the bare wire across the brass tacks, a simple linear motor "coil gun" was demonstrated. It didn't work too bad, actually. I think I did this sometime in 1994 or so.
Anyhow, what I had planned on doing was beefing up the coils (I had a ton of this wire - still do, actually), maybe 2-300 turns (or possibly buying a few pre-wound solenoid cores) - and wrapping them on a larger piece of tubing, perhaps some small diameter PVC pipe. In between each coil segment, I was going to mount a phototransistor/LED device to detect the passing of the projectile, and activate the coil ahead of the projectile for a set period of time; each one tuned to the reduction in time due to the increasing speed of the projective (likely to be a logarithmic pattern, I think). Another possibility would be to only keep the coil on for as long as the projectile is blocking the sensor, so that the coil turns off once the projectile passes the sensor, but before it has reached the center of the coil. It would've taken simple a large transistor and/or MOSFET, plus the sensor and a few other passives - actually a real simple circuit.
You could power the whole thing off of large capacity batteries, or if you wanted more "oomph", a small capacitor array for each coil and a charging circuit of some sort. It likely wouldn't have been that powerful, but it would've been a fun project. I ended up moving on to other things, and the demonstrator was eventually dismantled.