Is it possible to craft armor-piercing ammo yourself on the reloading bench, or can you only find/buy it?
Depends on the ammo type you want to create. For instance, you can't produce any of the specialty 9mm ammo yourself - it all has to be bought from vendors.
Specialty Ammo can be produced in the following varieties:
Additionally, all Energy Weapon cells (Energy Cell, Microfusion Cell, and Electron Charge Packs), can be produced in both Over Charge and Max Charge varieties for increased damage.
Note: many of these ammunition types, in addition to doing increased damage, will cause the durability of your gun to decay substantially faster. Use only as needed, and with caution!