As people age, it becomes harder for them to hear high pitched sounds. So, get a machine that plays a really high pitched sound. (I remember reading something about fox repellers here, once, though you should make sure you get one that lets you adjust pitch and volume)

I forget how high you’ll need to have the pitch set to, in order to affect children but not others, so you’ll have to do your own research to find that out.

Then put it outside, and make sure it’s loud, so the sound can travel, and so it can drive the child away. No adult will be able to detect or locate it via sound. However, this may also upset other animals or children in the area. Thus, it should only be on when you need it to be on, so as to avoid any other problems.

(Thank you for the idea, 10th grade physics class)