If you're racing dogs they use that stupid mechanical rabbit, obviously better than a real rabbit.
So what do they use for goat races? A tin can on a string dragged around in front of them? Actually with the way goats eat I'm guessing you could put just about anything on a string, even just a string, and they'd go after it...if they were in the mood.
Click on image to see it larger.
This image is badly glued into an old album.