You Craft Me Up! figured out how to make bows out of PVC (and the arrows are just dowel sticks with notches at the string end:
WARNING: These really work! The first time I made one, I tested it in my garage and put a dent in my garage door! These should NOT be used indoors! And instruct the kids to never point them at anyone, pets, or cars! So far my kids can’t really launch them far, so we haven’t had any problems. knock on wood! :)
Disclaimer: I am actually an archer and have some pretty strong opinions about archery safety, even with little kids wielding lightweight bows. I think this is a great project, but have to very strongly second her final suggestion: “If you want to make them safer, add a small piece of foam, or nerf arrows to the ends of the dowels.” Please definitely do this! The dowel arrows will still have some impact, but at least blunting the ends makes it much less likely they’ll hurt anything or anyone. As careful as your kids may be, pets and wild animals can still rush out unexpectedly into the line of fire.
You could also put suction cups on the ends so they might stick to some targets. You can even buy suction cup arrows for not much, but they probably aren’t as durable as dowel ones you make yourself.
And what should you have kids shooting at? The best option would be hay – what a lot of serious archers use. Stick a few bales of hay in the yard and put targets on them. The arrows can actually stick in the hay, so kids will enjoy that. You can search “free printable archery targets” and find plenty that will print on standard paper, which should be big enough for kids shooting from just a few yards/meters away.