Posted this in another thread but wanted to make a separate post for anyone doing a search.
How to unlock Cypher Weapons in Zereth Mortis
First you need to do the Jiro quests starting with Broken Circle. You will need Altonian Understanding from the Cypher Research Console to understand and talk to them.
Then you need to get a drop called Resonating Disc and turn it in to Olea Manu outside at Faith’s Repose FP(Firim’s cave). It has a relatively high drop rate from any enemy in the zone.
Olea Manu also sells some items for additional Cyphers including an item that increases Cypher drops by 50%.