This tip will only work on the first shot. The bird will then fly over the hole and drop the ball close to the hole. When your ball is right in front of the alligator in the Incredible Machine, putt your ball into the alligator's mouth. If you did it right it will be thrown either into or next to the hole. On the moon base hole, hit your ball into the metro station when the sign reads '3'.
Timing is VERY important.
Also, if you don't time it right, your ball will fall into the construction pit. Next to the pool of water across from the pyramid with the hole there is a bird. Putt the ball at the bird and it will pick it up and drop it into the cup. You can do this anytime anywhere. Keep hitting it in.