If you have craft lasers and Elerium Batteries (not just the prereq!), the only thing that can keep you from researching Laser Weapon Construction is not doing it in a lab with a Science Laboratory.
Otherwise, there are some armor-piercing kinetic weapons. Heavy Cannon AP rounds are probably the best of these, but there are several lighter kinetic cannons, too. Tactical Sniper Rifles. Miniguns strip armour. Chemoguns and Pulse weapon chem rounds both strip armour and do acid damage. Incendiaries at least take the enemy out of the fight for a little while.
Toxiguns and Canister Guns are alien acid weapons that don't require extensive interrogations to acquire.
