I’ve had cabrito at Mexican resturants and it was not gamey. My family had a gathering a few years ago and we purchased a young goat and barbecued it. I think the key is that it should be a young goat. The older ones might be a bit gamey, but even then I’ve heard that if you soak the meat in buttermilk it will take some of the gameyness(?sp) out.
I’ve also had curried goat in a Jamaican resturant that was done well. I think the spices helped with the flavor.