There's a limit to the number of fish that can be caught before the algae is triggered. To delay its arrival the only thing to do is to look for mushrooms and coconuts as much as possible, and avoid fishing. I was rather paranoid, and if I saw a villager going to fish I'd drag him/her away and set them on a coconut tree or on another task.

Only keep one trained farmer if possible and set the game to half speed when you're not playing. If possible check in often during the period so a) you can fix things if the one farmer gets sick and b) you find out quickly when the algae does arrive.