I've tried harvesting cherry trees, asking via wall post, etc. How do we obtain the cherries to craft farmhand for the quest? I'd rather not spend FV cash if possible. Thanks in advance.

Fill an orchard with cherry trees and harvest it. You don't have to spend farmcash - any cherry tree will do. You can 'find' items from harvesting loose trees too, but orchards give you a better rate of return.

Also, watch your neighbor's feeds. They may be sharing them when they harvest their orchards.