Tie a length of rope between two trees. With kids standing under the rope, tie pieces of ribbon to the doughnuts (one per player) and then to the rope so the treats hang slightly above mouth level.
Have players start on the count of three. Instruct each to eat an entire doughnut -- no hands allowed -- without letting it fall off the ribbon. The first to finish wins. There's no need for prizes; they've just been eaten.