Often times when fish stop eating it is due to parasites or fungal infections. Cichlids are often subject to internal parasites from their high protein diet, since they are not eating you will not be able to treat it with medicated food. Depending on the size of the fish you will want to move it to the smallest tank you can, so you can starting a dosing regime, you will want to use the smallest tank you can to save yourself on wasting medicine, my cichlid is about 2.5 pounds and 10.5 inches long and I put him into a 30 gallon when he needs to go to the "hospital". My large red devil cichlid has/had a parasite and he is on the tail end of his treatment and is already eating again, he did not eat or poop from March 30- April 11. What I dose my fish with Melafix and Pimafix, I dose both for 7 days, do a 50% water change then dose them for another 7 days, 50% water chance and then keep an eye on them for the next week, all in all he will spend 3 week in the hospital tank. You should also continue to offer them food, but at a greatly reduced amount, my cichlid eats roughly 15-20 pellets of food a day, and I would offer him 3 pellets a day till he finally ate. After they start eating you will need to slowly increase their foo intake, don't go dumping a bunch of food in there this will foul up the water, today is the 14th and he started eating on the 11th so he is going to get six pellets a day, three in the morning and three at night.
The main thing to keep in mind if you need to thoroughly clean the hospital tank and any and all equipment you use for it, heaters, filters, air line tubing, etc etc, with hot water and vinegar. This will kill off any bad germs or parasites that might linger behind. I also clean my hospital tank twice, once when I take it down and again before I set it back up. You will also not want to have any substrate in this tank or any decor be it fake or real. Also try and maintain the cleanest water you possibly can, I have a battery operated gravel vac so when I have a fish in there I can easily vacuum the bottom of the aquarium daily, takes less than 2 minutes. Also do not use any chemical filtration in your filter, just use physical, just remember to throw it all away when you are done. I personally use quilting batting from one of the big box stores and a $13 roll lasts me about a year or more for all my aquariums.
Discus are also usually very peaceful fish, they will fish back on occasion but usually they do not, at least from what people have told me. So if it is getting bullied you will need to take a few steps to help prevent the same behavior when you reintroduce it back into the main aquarium. The first time is you want to make sure you have PLENTY of hiding spaces, a good rule of thumb is at least 3 spots for each fish, so if you have 5 fish you need 15 hiding spots, it seems like a lot but a fish will have 1 main spot and several back up spots that it will go to if the first spot is compromised or they feel threatened. Another step if you only have one aquarium and do not have the option to move one permanently you could take is to decide which fish you want most, do you want the discus or do you want the bully? A good step to take, if you want to try and keep both the fish together again, is the day you want to add the discus back do a major rescape on the tank, if you have driftwood and stone move them completely, don't just shift them an inch, you need to make the tank as different as possible, this will put all the occupants of the tank on the same footing, no one will have an established hiding spot, or territory to dominate. Then when you go to add the discus turn off all the lights in the room and all the lights in the tank and add it in there in as complete darkness as you can provide. This will keep the bully from seeing the discus return to the tank and offer it a chance to find a spot for itself, when I had a big african cichlid tank I had to do this every time I bought a new fish, it can be a pain in the @#$ but it is well worth it if you want to keep your fish alive.
I'll add more info as I remember it. Also some better pictures would be very helpful, some close up shots, just make sure they are in focus.