I used to recommend keeping sickly discus, but after years of keeping them myself and finding that over time they seem to go downhill, I now recommend to cull. Culling is a hard thing to do at first, but ultimately it saves a lot of sufferring and pain and ensures your healthy stock stays healthy. I now cull my sickly fish and fish for my friends when needed, if I feel it is warranted.
I used AquaSed, a sedative that is used for fish surgeries and when overdosed it puts them to sleep very efficiently and euthanizes them. Some people used clove oil in the same way. Others do it quickly by chopping off the head. There are other methods but these are the ones I go with because they seem to be fairly painless (hopefully??). The method of euthanasia is an entire discussion in itself, and can sometimes get tempers flaring. Research online for yourself which methods are most humane.
If you aren't ready to cull, I would recommend separating them into a hospital tank away from your healthy fish and observing their progress/feeding/health etc