I know how you feel - I've been through some pretty poignant situations in the 18+ months that I've been working with these little villagers.

Only another villager can heal a sick villager, but even a child can heal him. I haven't tried this to know for sure that it will work, but what you might try is putting your game on 1/2 speed, which will slow down his weakening from disease. The slower speed might not slow down the frequency of Island Events, so you have a better chance of something happening that could help him.
I'm really rooting for the little guy, and I will rejoice with you if salvation arrives in a crate or barrel.
