I'd probably use the same technique I'd use if I was tandem abseilling with anyone, i.e. extend the abseil and attach both parties to it:

     |
     |
     @<- belay plate
    / \\
   /   \\ <- rope to adult
child--adult
      ^   |
     /    | <- tail of rope
    /
  attach child to adult as well as rope for safety

So you extend the belay away from yourself, and attch both parties to the belay, also attach the child to your harness as a backup (don't drop the baby). You then belay as normal (keeping the rope away from the child).

Add a prusik backup (don't drop the baby!!)

I actually found a photo of a similar set up:

no backup though on the above photo...this is bad, don't do this...(please don't drop the baby)

I'd probably use the same technique I'd use if I was tandem abseilling with anyone, i.e. extend the abseil and attach both parties to it:

     |
     |
     @<- belay plate
    / \\
   /   \\ <- rope to adult
child--adult
      ^   |
     /    | <- tail of rope
    /
  attach child to adult as well as rope for safety

So you extend the belay away from yourself, and attch both parties to the belay, also attach the child to your harness as a backup (don't drop the baby). You then belay as normal (keeping the rope away from the child).

Add a prusik backup (don't drop the baby!!)

I actually found a photo of a similar set up:

The black rope going east from the adult's harness tie-in is also tied to a second karabiner on the child's harness and then up (behind the pink sling) to the safety belayer.