I fight this problem too, it's one of the downfalls of outdoor growing. I either have to water almost every day when it doesn't rain, but when it does rain it seems to never stop and causes issues.
The ideal situation would be to cover the plants so you can control moisture. This is tricky to do and still get adequate light. An alternative is to use a systemic fungicide like Captan. Physan is good as a preventative measure but it's not heavy duty enough for these dire situations.
Once a plant is affected, it is tough to "cure." The best option is to remove the affected tissue, sterilizing the blade between cuts. You can dust the cuts with cinnamon or seal it with a slurry of cinnamon and elmer's glue. Sometimes removing bad spots can mean unpotting the whole plant and cutting away the bad parts at the rhizome.