Another trick is to squeeze lemon juice into a cup of water, and give the apple slices a quick bath in there after you slice them.
I do thisall the time but with orange juice. It works, and there is no sour taste to the apples.
However, a lot of times I don't even bother. If you put the apple slices in a ziplock, they don't turn all that brown, and they taste fine, as long as your kid doesn't mind that they're a little brown. Another trick is to use one of those apple slicers that slices the whole apple & takes out the core - sometimes I do that and put the apple back together, including the core and wrap in a piece of plastic wrap. If all the slices are touching and not exposed to air, it doesn't turn brown and your child can just unwrap, eat the slices, and throw the core away.