I usually kill Cyberdiscs with the Rocket Launcher and Large Rockets.
Its the only early game weapon, which is avaible from the start which has a 33% chance of killing them instantly on Superhuman difficulty.
Cyberdiscs do have 38 Armor in all directions on Superhuman, they also only take 60% of damage from explosives, but since they are a 2x2 unit, they do take 4 times the damage on a direct. Also they do not explode, if you kill them with Large Rockets.
Conventional Rifles will also withle them down over time, even on Superhuman but you need a lot of shots (38 armor with 0.8 damage from AP weapons and 120 HP vs Rifle damage of 30).
Of course once Laser Rifles are avaible, those are the prefered way of engagement vs Cyberdiscs.
On any difficulty they actually lack the ability to down those in one shot thou.
Thats why i always have 2 Rocketeers on my Combat teams, equipt with a full load of Large Rockets, i even have some preloaded spare Rocket Launchers and some spare Large Rockets in the Skyranger on top, you never know, when you need the extra firepower