Lies Of P Overture, like in the base game always makes exploring all corners of the world worthwhile by rewarding you with useful upgrade materials, weapons and other interesting loot. You should not miss out on collecting all 4 Carnival Coins as well, and in this guide we tell you exactly where to get them from, and the rewards you get for each of these.
Carnival Coin #1 Location

Reward: Tap Dance gesture
Start from the Carnival Garden Stargazer, and enter the Carnival. Take a left and you will come across the 1st Carnival Coin next to the central memorial-like structure, near the carts. Enter the building on the left, and you will see a closed door next to the ‘Carnival Prize Announcement’ collectible.
As you approach it, you will get an action prompt to ‘Insert a coin to activate’. Watch the small dance scene, once it is done you will get the Tap Dance gesture as a reward.
Carnival Coin #2 Location

Reward: Maniac Pinwheel Blade + Handle
Enter the Carnival, and proceed straight ahead to fight the Maniac, who has a similar moveset to the first boss fight in the base game. Defeat him to get the 2nd Carnival Coin in Lies Of P. Proceed straight ahead to the Clown Circus arch, and insert the Carnival Coin at the stall manned by a green-dressed puppet. Enter the door on the right, and stand on the lit central stage. Hit the 3 puppets that pop up, avoiding the red glowing one as it explodes; and collect your reward.
Carnival Coin #3 Location

Reward: Workshop Union Auto-adaptive Converter +2
Move towards the Ferris Wheel, and take a left towards the Merry Go Round. Collect the 3rd Carnival Coin from the left side of this ride. Go back to the stall where you used the 2nd Carnival Coin, and this time you will face the annoying Joker type enemy that was your bane in the base game. Defeating him gets you a nice Ergo Crystal, and opens up a locker straight ahead to collect your reward.
Carnival Coin #4 Location

Reward: Full Moonstone of the Covenant
Enter the Carnival arch and take an immediate right. Go to the very end, and proceed under the walkway bridge to collect a Star Fragment and the 4th Carnival Coin. To redeem this, you need to go to a different place and not where you got the rewards for the 2nd and 3rd coins. Go towards the Merry Go Round, and take a sharp left and straight ahead to an open door next to a cutout of a set of balloons. Insert the final coin to collect your reward.
Here is a handy video that has the full details:
While you are in this location, don’t miss out on the Rosaura side quest as well.