Cucumbers, zucchini, squash, melon, tomato, basically any vine veggie/fruit that's safe for chickens to eat!
We did green beans directly in front of the run this summer, which aren't safe for chickens to eat raw in large amounts, but the girls didn't have much interest in them. They ate pieces of the leaves occasionally but not enough to get sick, and left the beans alone. They also ate some tomato leaves, and both green and ripe tomatoes from the garden without consequence.
I think there are thornless rose varieties. Raspberries are another option. The only worry I really have with thorns is around the face, since feathers protect their bodies. We've had some scrapes and scratches from the wild raspberry and other thorny bushes growing around here but nothing serious.