In order to get the Unique Weapons you need to bribe Deputys and Crime Lords enough to be able to buy the weapon from them. When you start a mission and it says Unique Weapon you actually need to buy them in that mission from those people. So, if the mission start screen says that there are three unique weapons that means there will be three Deputys or Crime Lords on the map that you need to buy the weapons from. The unique ones are the one with the start like the "Sir Jury" pistol or "Chicago Piano" tommy gun. Ones with one, two or three dots with names like "exceptional pistol" are not unique...
Well I get up in the morning and I get my brief. I go out and stare at the world in complete disbelief. It's not righteous indignation that makes me complain. It's the fact that I always have to explain. - Van Morrison