Covenant Item Farming Strategy
Since this is a platinum guide, I am not going to describe where each covenant is. Instead this guide will tell you where I had the best luck grinding out the covenant items to rank up.
First, I want to say that for at least 50% of the community the auto-summon covenants are completely broken. You aren't alone if you put on the Way of the Blue, Watchdogs of Farron or Blades of the Darkmoon and don't get summoned. It is a well known and well documented problem. Nobody is exactly certain why they work for some people and don't for others. There are a couple of things that are confirmed to help though: soul level and max weapon level. When the game tries to match you up with someone else when auto-summoning it takes these two things into consideration perhaps more than anything else. Most people agree that SL 40-70 or so will have the best results for being summoned. This seems to be more important than your max weapon level, but the game will take that into account as well. Note that placing your +10 Dark Sword into your item box or unequipping it will do nothing for matchmaking. Once a weapon is leveled up the game will save that information to your character profile and use it for matchmaking even if you are holding a +0 Thrall axe and sold your +10 weapon to the handmaid. With this all being said, most of us really are left with one option for these covenants and that is to grind out the drops from specific mobs in the game. This is a LONG and tedious process that will make you want to pull your GD hair out at times. You are also going to be absolutely rolling in souls which I guess could be a good thing depending on who you are.
Something that I started to notice over the course of many hours farming these items is that there does seem to be a way to "force" the game to drop the stuff at a higher rate which will help a ton. What I have found is that for whatever reason starting from a "fresh" session seems to result in an item being dropped within the first 10 farming cycles. I don't really have any idea why this works, but I have tested it extensively on the silver knights at Anor Londo and it definitely is noticeable. I have seen other suggestions out there ranging from changing your armor every time a needed item drops to using multiple rusted coins for each cycle, but for me nothing aside from completely exiting the game and starting back up seems to make a difference. However, since this is not science, if you notice something that seems to work for you, keep doing it!
My general process for farming is to start (again) from a "fresh" session and start farming. Usually I will have a Proof of Concord Kept within a couple of minutes. Once I get one I will keep going for a few more (10 or so) minutes and if another doesn't drop, I will quit the game, close the application and start again. Following this method I was able to get 11 Proofs in about 2 hours last night alone. Something that seems to derail the process when starting from a "fresh" start is dying. Being killed seems to reset loot drops or drop percentages. That being said, I have also noticed that after going a long stretch with no drops and then dying, I received a Proof shortly after.
* What I mean by "fresh" session is that you are starting the game fully and not coming back to a suspended state by putting the PS4 in rest mode.
* A farming cycle is going from the bonfire to killing the mobs and back to the bonfire to force the respawn.
As far as your loadout and equipment for farming you really just want to set yourself up so that you can cycle through as fast as possible. Faster kills=more chances for drops. I will give a short description of what I was using in the area for the applicable covenants. You should have around 350 item discovery or more for the best results. That means you will need to have a Covetous Gold Serpent Ring, Symbol of Avarice (helmet) and a Crystal Sage Rapier. Equipping these items and using a Rusted Coin before each cycle should give you about 350 Item Discovery.