OK, Alien Guns are definitely NOT the easiest of weapons to get, infact some people may spend from 20 minutes to 7 hours hunting for one doing the method I'm about to tell you, it is possibly the most efficient form of hunting for an Alien gun.
I'm pretty sure you have arrived at New Haven, if not, I don't know what your going to do, I'm sorry, well, assuming you have got to New Haven, the first thing is to learn the locations of the weapon crates throughout New Haven, search "New Haven Weapon Crate Route" on Youtube or something, I'm pretty sure the most efficient way of getting around the Weapon Crates will be there. You collect all the Weapons from the Weapon Crates, sell any extras you don't need...The weapons in the crates are absolutely random, if you repeat these steps by exiting and re-entering the game after collecting all the weapons from the crates and selling them to a vendor machine. Sooner or later you will get an awesome Eridian Weapon gun.
SECOND METHOD BY Agitokatana - Master MCloud in Crimson Fastness has a guarunteed drop of an Eridian Cannon, which fires a slow, high damage bullet at the target. It should also be stated that Red Oval Chests and Master MCloud are the only methods of getting an Eridian weapon.
FYI - eridian weapons are much more common after you beat the game and start a Second Playthrough.