Check out this tutorial on how to make your own slingshot ball for your dog or for a gift. The cheapest store-bought version, like the Go-Frr Ball, that I can find is $8.00. You could probably make eight DIY slingshot balls for the same amount.
You’ll need some rubber balls—I’ve seen multi-packs in toy stores or you could check a dollar store—and you’ll need some surgical tubing, which you can get at many hardware stores. For tools, you’ll need a drill and a wire coathanger. A batch of these would make a nice gift.