From your comments, "there is no set discharge period that I have." This basically means we can't provide a solution. It's the electrical engineering equivalent of "I want a vehicle that moves fast, but I don't really care how fast." The best vehicle choice varies greatly from tricycles to SR-71's and space shuttles.
I can point out that, as a general rule, the slower you allow the discharge to be, the more convenient your technology is. Things that can discharge in a millisecond tend to store less energy per kg (specific energy) and store less energy per cubic meter (energy density).
Three technologies that might be on your list (energy density numbers from this wikipedia page):
- Film Capacitors - These are fast discharge (microseconds to nanoseconds). However, they are very poor when it comes to energy density. There's literally orders of magnitudes difference between different film capacitors, but they are somewhere around 10J/kg
- Large Electrolytic Capacitors - These are slower discharges because they can heat up and boil their electrolyte. There's, once again, literally orders of magnitude differences between different products, but if you stick to microsecond to millisecond discharges, you're probably fine. Energy density is somewhere around 200J/kg
- Supercapacitors - Once again, slower discharge, but more efficient. The specific power of a supercapacitor is lower than that of an electrolyte capacitor, so it can't discharge as fast. However, it's energy density jumps to 10-40kJ/kg
- Batteries - Battries discharge even slower, but jump to 170kJ/kg (lead acid). The highest battery on my list is a lithium metal battery at 1.8MJ/kg
Now what you should note here is that all of these numbers are small. Even using the most dense energy storage on the list, batteries, you're talking 70 million kg of batteries. That's roughly the mass of a Nimitz class aircraft carrier.
You didn't specify how big your spacecraft was.
You could try storing your energy in a superconducting loop. If you did that, there'd be no resistance. However, there is always a finite chance of any one section of the loop becoming resistive. The more energy you put in the loop, the higher the risk. If any one section becomes resistive, it quickly heats up the nearby area and a "quench" occurs, where all of the energy is dissipated immediately. This is something they deal with in particle accelerators. As I have heard it described, they have to work a balance. Quench too many times in a day, and you don't get enough work done. Play it safe, use low energies, and don't have any quenches, and the results aren't interesting enough to warrant the huge cost of the collider. They have to find the right balance.
Sadly, I do not have numbers for predicting how much energy you could reasonably store in one of these loops. I do, however, have stats for the LHC. The circuits powering the magnets in the LHC have about 10GJ of energy in them (a small fraction of what you need, but useful none the less). When a quench occurs (typically due to something stray in the beam, but sometimes its due to random effects in the magnets), it takes about 2 minutes to dump all of the energy into a steel block -- it heats 8 tons of steel about 300 degrees in those two minutes.