I completely forgot about your pictures until I played Super Mario Galaxy earlier today, Toad. I'm sorry for the wait, but I got them all! The Sling Stars can only be found in the second course, which is located in the Loopdeswoop Galaxy on the star, "The Galaxy's Greatest Wave."
This is where the sling star would be once you beat the course.
After completing the course and seeing the star...
...move back to that same spot to find a Sling Star!
After going on the Sling Star you will touch a ? Coin.
The ? Coin will reveal circles of Star Bits for you to collect!
After the first Sling Star you will land on a platform that has a tree, a penguin, and another Sling Star.
After going on the second Sling Star, you will go through another ? Coin and collect even more Star Bits. You will eventually land on another platform. Unlike the other one, this one doesn't have anything on it except for a Sling Star.
After going on that Sling Star, you will end up back where you started.
I hope that cleared things up for you!