Our kids have been rather ill for the past two weeks.
Our daughter, especially, didn't have an appetite. That's no surprise for a sick child. Much more important is keeping them hydrated when they are ill.
An easy way to do this is by having a tea party! My children had four or five pitchers of water during their tea party, and most of it was drank by my sick daughter. (E wasn't sick at that point.)
We love our little pitcher set from Tupperware. It's perfect size for young children to pour themselves and was great for E when he was first learning to drink from a cup.