This is one of those times where a press camera comes into its own.
I've shot several sheets of our young child with my MPP Microtechnical camera. Set the focus, then with an aperture of around f8 and suitable shutter speed (according to film speed), use the RF to confirm the focus. Framing can be a bit loose, since there is plenty of film real-estate to play with.
I'm sure that using the string option would work too, especially if the end of the string had something nice a bright to get the child's attention. Have the camera pre-focused, pull the string away at the last moment and shoot.