Set up two areas in the yard - one with eggs and one without eggs.
Using a child-friendly Bible tell the crucifixion story up to the point where Jesus was put into the tomb. Now send the children to hunt for eggs in the part of the yard where there are none to be found. When the kids have spent some time hunting without success, talk about their disappointment and sadness and relate it to how the women must have felt when they went to find Jesus in the tomb and He wasn't there. Then say, but this is Easter and Jesus is Risen, lets really celebrate. Now go and find the eggs that have been hidden for you! Once the eggs are found, read the resurrection passage from a child-friendly Bible.