I'm thinking it's more likely that you are dealing with a respiratory infection rather than coccidiosis. The mucous from the nose or mouth would be more likely respiratory.
If you can get a vet to do a blood test you can find out what it is. Most respiratory infections are not "cured", the bird may recover but will remain a carrier for life. And any time they are stressed they can become symptomatic again. And they can infect the other birds, most respiratory ailments are highly contagious.
Antibiotics can help with any secondary infections but will not do anything for the virus itself, assuming it's a respiratory virus. If a bird is weakened it may also allow other infections to take hold, like coccidiosis, so it's possible that they develop both.
Runny droppings could also be caused by internal parasites, which could also weaken the bird and leave them more at risk of other disease. If you can get a fecal float test done it would identify any internal parasites or coccidia, and determine if treatment for those is necessary. Hope that helps.
If you can get a vet to do a blood test you can find out what it is. Most respiratory infections are not "cured", the bird may recover but will remain a carrier for life. And any time they are stressed they can become symptomatic again. And they can infect the other birds, most respiratory ailments are highly contagious.
Antibiotics can help with any secondary infections but will not do anything for the virus itself, assuming it's a respiratory virus. If a bird is weakened it may also allow other infections to take hold, like coccidiosis, so it's possible that they develop both.
Runny droppings could also be caused by internal parasites, which could also weaken the bird and leave them more at risk of other disease. If you can get a fecal float test done it would identify any internal parasites or coccidia, and determine if treatment for those is necessary. Hope that helps.

