We use 2 KOP compressors to charge our tank. It still takes a long time to charge from 0PSI to shooting pressure, but we can get 3 shots out of the tank before having to wait again.
We are using an old freon tank used to charge air conditioners that was empty. It's a bit large for our use, although I can't think of any other tanks that would work better.
For the sprinkler valve, we connected 3 9V batteries together in series to a relay (not a spike) and connected the relay to a spike. This gives the sprinkler valve 27V of power, which shouldn't hurt it at all (and hasn't hurt it over the past 4 years). We put a software limit on the amount of time the shooter can shoot which saves on air and charging time.
The example
above me is pretty much the system we use.