What's wrong with conventional firearms? Modern sniper weapon systems are reasonably reliable, powerful, and accurate to over a kilometer depending on caliber. A rail gun that can be safely fired from the shoulder isn't going to be any more powerful than existing chemical propellant rifle technology simply due to Newton's third law. If you increase the amount of kinetic energy going down range and you'll increase the kinetic energy being transferred into the shooter's shoulder by the same amount. The energy going into the shooter is just transferred at a slower rate due the inertia of the gun itself. Force = Mass * Acceleration. The bullet has low mass relative to the rifle, so it is accelerated to a much higher velocity and thus delivers its energy to the target at a concentrated point in a very short period of time. The rifle has high mass relative to the bullet, so it is accelerated backwards into the shooter with an equal force, but at a much slower velocity, and it is spread out over a much larger surface area.
Additionally, until batteries come to match the energy density of modern smokeless propellant(even including the mass of the metal casings), your snipers are going to be lugging around more weight per shot (all else being equal) than if they used conventional ammunition cartridges.
However, if you really don't want conventional firearms for whatever reason, maybe you can look at micro-rocket propelled projectiles. Bullets are unpowered, they start dropping as soon as they leave the barrel/rails/coils of the weapon, so the shooter has to compensate by either zeroing the sights for a specific distance or using hold overs for various distances. A gun that fires microrockets would, in theory, have a flat trajectory. This was tried in real life in the 1960s with abysmal results. The Gyrojet had to accelerate to lethal velocity over several dozen meters (if you shot someone at spitting distance with it, the projectile would bounce off harmlessly) and suffered from wild inaccuracy. However, if the concept were revised to use a conventional firearms cartridge to initially propel the projectile to lethal velocity, then engage its rocket motor and fly the rest of the way to the target under its own power, you might have something. The rocket projectile might even be guided.