Concrete! Involves a chemical reaction that would further damage the plant. Comet! - the kind I scour my sink with?
How deep does the rot go? Cut the rotting branch back with a clean sharp knife - cut off a little at a time until you find tissue that is green (no brown). You will have to sterilize the knife after every cut with alcohol or you will transfer the rot to newly cut parts. Keep cutting until you find healthy green tissue. If you cut all the way back to the trunk and are still seeing brown, the roots are involved and you will be saving pieces of the plant.
PS: