For small children we provide infant life jackets (basically under the age of 4).
Anyone else gets the standard adult life jacket. I've had children in them before and they worked fine. If anyone inflates a life jacket in the cabin our manuals indicate we are to remove that life jacket and stow it in an overhead locker and provide that person a new life jacket. My airline is very strict on inflating the life jacket only once outside the aircraft (eg. jumping out of the aircraft door).