There are 3 or 4 necklaces that help healing skill, maybe more. Master Healer or Perfect Villager are the two obvious ones. The others that give adept healer aren't as much help but if you only have one healer and you heal aggressively, you can do it. Be sure to have healing skill checked on one and only one healer and leave it checked overnight and when you're away from the game for hours. Try with the youngest adult you have when you have middle-aged to old villagers - they get sick more often. Use adults to catch frogs because they have a chance to get sick from it.