I tell them I hate them more.

I tell them "that hurts my feelings because I like/love you so much. I can see you are very upset, but it isn't ok to speak to me like that. Why are you feeling so angry, sweetie?"

I always say "that's fine, I still really like (or love) you". Kids say all kinds of things and they have to be of a certain age before they understand how their words affect others. It's fine to state what is OK and not OK to say to someone, but they might not get it if they are under four. Also, keep in mind, when a child says "I hate you", what they are really saying is "I feel like I hate you right at this moment because I am not getting my way or I feel angry but don't know how to express myself". Don't take it personally.

Very calmly and firmly state that is not an okay thing to say to someone. For the younger ones explain that saying you hate someone is mean and hurtful. For older kids You can go into a more in depth discussion. For instance ask why they are saying they hate you and then come up with another way for them to express their feelings. I think it's a good idea to talk with all the children about what you could do to make your time together more fun and go from there.

...one of your charges says they hate you?

Specifically when they say this early in your relationship, so not a child you've known for ages who's going through a phase, but when you're still trying to build a positive rapport with a new child.

What do you say to a 3 year old who says it? A 6 year old? A 10 year old?

All approaches and ideas are welcome!