What tech would be needed? Extremely good power sources.
The muzzle energy of a 0.45 pistol is around 560 joules per shot. An AA battery contains 12,000 joules. Or enough energy for about 20 shots under ideal situations. However, with every mass-based weapon, at least 50% of the energy goes into recoil, and as soon as you introduce the circuitry of a typical coil-gun, you're even lower. This guy measured 2-3% effective efficiency from stored->projectile, so not even the charging. Now if 12,000 joules is all used in one shot at 2% efficiency, we've gone down from a .45 round to a .22 round. Eh, maybe use a lithium cell instead of an alkaline!
Even this is slightly ideal because an AA battery has less capacity at higher currents, so if you want a good refire rate, you'll need more batteries for the same output energy. But at this scale, it's at least feasible. A particle-beam pistol could be a viable weapon. (Note: it is hard to actually do this energy conversion. Coil guns typically aren't run on a single AA battery even if they only output energy in the 1-2Kj region)
Hold on, I asked about particle accelerators and you're talking about coil guns and pistols
Coil guns could be seen as a simpler and slightly more ideal form of particle accelerator. You put all your energy into accelerating the projectile. In a particle accelerator, you first have to ionise it. The projectiles travel faster, but the energy dealt on impact determines the damage done.
Now let's talk explosives. 1kg of tnt is equivalent to 4 million joules of energy. An aim-9 sidewinder missile's warhead weighs 9kg, and I'm willing to be it's got more than tnt inside it. But let's just assume that our aim-9 missile can output some 40Mj of destruction.
Allowing for our 2% efficiency from earlier, we need an electrical source providing 20Tj of energy to deal the same amount of damage. The engine from a 777 airliner outputs 83,164 kW, so to fire our weapon we have to be running that airliner engine for around 67 hours. An airliner burns tonnes of fuel per hour. Needless to say, the extra energy required to manoeuvre those tonnes of fuel vs carrying 10kg of high explosive?
So how about nuclear reactors then? It's very hard to estimate how heavy a reactor is (and in space, it's all about how much it weighs). The RTG's flown on existing spacecraft are measured in the 100's of watts, so you'll be charging your guns for years. However, if we have a pair of nimitz's nuclear reactors (550Mw), then we can squeeze off a shot every twenty seconds. Still, two A4w reactors aren't light-weight, and one shot every 20 seconds is pretty pitiful.
In short: you can stock a lot of missiles for the same mass.
So if you can hand-wave a good powersource that isn't more destructive by itself, then you can have your particle guns. (Is a fusion reactor powered particle accelerator more destructive than a fusion warhead? How about an antimatter reactor vs antimatter warhead?)
So where might a particle accelerator be useable even on the large scale? A large space station will have several large reactors powering it's internal systems (eg heating). In a period of combat, the life support can be turned off (everyone get's into their spacesuits), and they power up some particle accelerators.