I have done a few shots of children advancing towards me, walking, running and even cycling. Typically (but not always) outdoor. This experience is somehow similar to yours although the moving object might be different.
I obtained (what I deem) my best shots using MF lenses (or AF lenses set in MF) for which:
- I pre-determined the focus distance (on the focus ring) at a distance between myself and the start of the children run/walk,
- I set the shutter speed to at least 1/20s (or 1/60s) for walking (or cycling) kids running straight at me; I use shutter priority (P mode+ force manually the shutter speed)
- I use Hi continuous shooting.
It is possible to use Catch in Focus (CIF) with walking children but it does not work with running or cyclings kids. (Trust me.)
Note that, for automative objects like cars and bykes, the above will work although I would use a faster shutter speed (1/1,000 s or faster).
I hope that the comments will help....