Looking ahead a bit to the possibilty of a new visibility system, a dedicated sniper type might be a neat idea. With extended vision range compared to other units, and possibly limited ability to see through smoke (if any future visibilty system supports that) they would be better than other aliens (and probably a little better than PHALANX troopers) at acquiring targets. They should prefer accurate weapons over more damaging ones, and crouch and use aimed fire more often, to maximise their hit chances.
On the minus side, they should be physically quite weak (low HP, low natural armour), unable to wear heavier armour, and especially vunerable to flashbangs (due to oversensitive eyes, similar to the Tamans stated vunerability, although probably for slightly different reasons), but quite resistant to stun. They should also be quite rare, appearing at quite a late point in the alien progression, and only normally present at all on larger UFO types, and generally only in small numbers then. They would effectively be deployed as a Marine contingent on larger UFOs, providing long ranged support to the run'n'gun Ortnoks, and heavy firepower of the alien tank units.
Since they are introduced later in the alien ranks, they should have quite a range of weapons to choose from anyway, but it might be appropriate to also add an additional weapon just for them, with relatively low damage, high accuracy and only aimed and snap fire modes, and a medium TU cost. The objective is to model a Designated Marksman Rifle, *not* a true sniper rifle.
Doctrine is to use several well placed shots to kill / wound, not volume of fire. The weapon should still do appreciable damage to end-game PHALANX armours, around 80 points wth low variance perhaps - enough to allow a one-shot on low HP troopers with no armour, and still enough to worry a high HP soldier with good armour if he cant find and deal with the shooter quickly. Preferred method of attack would be to sneak out of cover and take a snap shot or two at mid range, or stay fairly still and take a couple of aimed shots at very long range. Unit TUs should therefore be fairly high, but not outrageous. It should probably have a fairly small clip as well (more like the 8 rounds of the bolter than the 30 of the AR).
As a comparison, the human sniper rifle does 105 damage (more than proposed for the new weapon), and costs 12 and 18 TUs to fire. If the "alien sniper rifle" takes the same TUs for the same fire modes, giving the sniper unit around 40 TUs would seem reasonable. That's faster than most PHALANX units, enough to fire 2 aimed shots whilst retaining a minimal ability to move, crouch / uncrouch, or 3 snap shots, or quite a bit of movement plus a snap shot, and so on.
The total *maximum* damage output / round would be around 240 (3 snap shots). If the best PHALANX armour had a resistance against the damage type of 50 (which seems possible given the planned progression of armour), that would bring actual damage from 3 hits down to about 90, enough to worry even the toughest trooper, and kill weaker specimens.
That would however almost certainly leave the sniper stranded in the open, though. Note that 3 shots at 12 TUs consume 36 of a max of 40, leaving a max of 4 left (enough to walk out of cover in a straight line, shoot 3 snaps, then take a 2 TU step back, or crouch before shooting from an exposed position, but not to move whilst crouched, then shoot, then move back into cover, for instance). Clearly, sniper AI should prefer to either aim to end a turn in cover and take what shots that TUs can be spared for, or try and stay at long range to take advantage of their superior range and accuracy
Although there is little firm detail about the proposed psionics system, I suspect using a psionic scan of some kind would be one of the best ways to locate these little monkeys, or UGVs whose relatively thick armour should serve them well here, enabling them to soak up several hits without undue damage.
Whether any new weapon is considered or not, the alien sniper would fill a gap in the aliens tactical makeup, allowing them to compete better in long range engagements, which is currently quite a weakness for them. They would logically spawn outside a UFO more often than other types where possible, to make maximum use of their talents.
If a specialised weapon was added for them, perhaps it should only unlock considerably after the snipers have started appearing, to give PHALANX a decent chance to get good armour and weapons fielded. These guys should certainly be scary, and able to punish sloppy tactical play, but not ubersoldiers with instagib guns.
Thinking about it, under the proposed health / medikit changes, an accurate, low-damage weapon would make even more sense for the aliens, since you'd have a fair chance of a soldier who has been hit several times having several bleeding wounds, and needing very swift medical attention to stop them from bleeding out, taking not only the wounded soldier out of the line, but also the soldier, or soldiers, needed to do the doctoring, possibly for several turns