You could also use Local/Group Policy to restrict the child's printing, IF they have their own login account that's not administrator. You can "restrict times/days user is allowed to print" to simply no days and no times.

Disabling spooler for just that user (via startup script? check the 'sc' command line for stopping services) is probably the easiest way.

Or, make them use their allowance to buy their own printer, ink and paper. They can save up for a $50 printer, but they couldn't afford to pay $20/cart for ink!