There are thirty coins to be found in Pinna Park. Ten are in the beach area and the rest are in the park itself, and since the park is closed in some episodes you can't get to them then.
Visible, beach (x6)
There are six baskets scattered around the beach, all are upside-down and have a coin visible inside. The only time you can get at them is in episode 2. Stand on top and wait until one of the purple Bullet Bills starts to track you. Hop out of the way just before the bullet hits the basket (to avoid getting hurt). The bullet blows up the basket and and you can get the coin. The black and gold bullets also blow up baskets but since they don't track you it's impossible to control where they land. With a couple of the harder to reach baskets you may have to stand nearby and then get the bullet to chase you to the basket. Visible in all episodes but only reachable in episode 2.
Visible, park (x6)
Pirate ship ramp
Enter the park and go to the start of the pirate ship ride, see the walk-through for episode 3. At the ramp, instead of boarding a ship, drop into the water and find the blue coin floating inside the ramp support. To get it, hop up from the water and start hovering until you reach the coin. Moving around might be better than hovering straight up. This may require several tries but you can ground pound right before falling to get the last bit of height. So this one is largely a matter of persistence. Available all episodes except 2 and 4.
Pirate ship cage
Enter the park and from the ride staircase that leads up to the two rocking ships, jump across to the second ship and ride it up to the left as in the episode 3 coin hunt. When it has enough momentum to reach the platform above grated box, stand near the front, hop and hover over to it. Pound the gate in front to get inside the cage and collect the coin there. It's likely you will get this coin without trying in episode 3. Available all episodes except 2 and 4.
Pirate ship platform
From the cage mentioned in the Pirate ship cage section, get to the top of the cage. You now need to get to the platform directly overhead. Wait until the pirate ship is about to make one of its complete turns (this happens every three swings), the hop on the front end of the hull for a boost, hop off, and hover to the platform. Don't worry if you don't do it the first time since this one of the more difficult pieces of acrobatics in the game. It looks like it would be easier to jump onto the square tip of the bow, but the hull is a lot easier to land on and you you probably won't slip off. Once on the platform get the coin which is just sitting there. Available all episodes except 2 and 4.
Pirate ship frame
From the top of the cage Pirate ship cage section, look carefully at the green frame that's holding up the ships. On the near corner on the right notice a blue coin. Hop and hover over to it. Available all episodes except 2 and 4.
Above pirate ships
Get to the platform where you collect the shine in episode 3, see the walk-through for that episode. You can spot the coin floating a bit below to the right. Hop and hover until you're over it, then drop to collect it. You will probably land in the water so don't worry about falling. Available all episodes except 2 and 4.
Enter the park, go right past the clam shells and under the orange arch. Continue up the slope until you reach a gazebo with a blue roof. Starting in episode 5 there is a bridge that leads from here to the start of the roller coaster ride, but in episodes 1 and 3 you can hop and hover over the gap where the bridge would be. Hover around to the ledge in back to find a coin. Available all episodes except 2 and 4.
Graffiti, park (x9)
Note that there is no graffiti in the beach area.
Enter the park, go right past the clam shells and find a graffiti M on the left side on the orange arch. Wash off the M and a blue coin pops out. Available all episodes except 2 and 4.
Enter the park, go left past the merry-go-round and reflecting pool, then follow the ramp to the fountain behind the Ferris wheel. This is where you're supposed to climb grates and fight koopas in episode 5. Check the far wall, above the block that sticks out, to find a graffiti M high above the ground. Wash it off for a coin. Available all episodes except 2 and 4.
Park rear M
Enter the park, go left past the merry-go-round and reflecting pool, then drop to a sandy area behind the pool. Check the wall near the tree there to find a graffiti M. Available all episodes except 2 and 4.
Paired crosses (x2)
Enter the park and locate the graffiti cross on the right side of the wall between the pirate ride and the reflecting pool. Then locate a corresponding cross on the tree next to the path leading to the gazebo, the tree resembles a giant Pianta head. Wash one cross off to make a blue coin appear at the other cross, then quickly get to the other cross to collect the coin before it disappears. Hover across the pool under the pirate ride, quickly hopping out to continue hovering when you fall in. Available all episodes except 2 and 4.
Paired triangles (x2)
Locate the graffiti triangle on the wall above a small ledge behind the pirate ride, then follow the ramp leading from the gazebo to locate the corresponding triangle on a wall near where people would board the Ferris wheel. Wash the graffiti and rush to get the coins. To get from the upper location to the lower one just drop down ledges, but to go the other direction you need to do some fast back-flips. Available all episodes except 2 and 4.
Paired circles (x2)
Get to the top of the Ferris wheel, see the episode 5 walk-through and locate the graffiti circles on the left and right. Wash and get to the other location for a coin each. This time the symbols are fairly close together so it's more a matter of not falling off here. Available all episodes except 2 and 4.
Miscellaneous washing, beach (x2)
Sand icon (x2)
There are two spots on the beach where washing the sand reveals a blue shine icon. Keep washing and a blue coin pops out when the icon is complete. Keep watching for sparks in the sand to find these, since you will be spraying the sand to find fruit and coins anyway. Both are located in front of the sunflower area. Available all episodes.
Miscellaneous washing, park (x3)
Blue parrot (x2)
There are two blue parrots in this level that each turn into a blue coin when sprayed. One likes to perch near the merry-go-round and the other near the gazebo. Wait in those locations and zap any birds that come close until you get all of them. Available all episodes except 2 and 4.
Go to the clam shell ride and spray the green clam shell until opens. Grab the coin before the shell closes again. Available all episodes except 2 and 4.
Tower of Stus
Enter the park and go past the merry-go-round to the reflecting pool. Check to the right to find a stack of Stus (round creatures with short legs). Spray off the ones on the big one, then hop on top of the big one to defeat it and get a coin. Available all episodes except 2 and 4.
Yoshi needed, beach (x2)
You need to get Yoshi before the Yoshi egg appears and you can get these coins. Yoshi appears in all episodes here, but only after clearing episode 5. So you can return to episodes 1 through 4 and find Yoshi after completing episode 5, but Yoshi will not appear the first time you go through these episodes.
Get Yoshi and hunt for butterflies in the sunflower area. Fruit can be had by spraying the sand, but it may take a while to find the type of fruit needed to wake up the egg. Have Yoshi eat two of blue butterflies to get a blue coin for each.
Yoshi needed, park
Yoshi is only found in episode 6 here. (For some reason Yoshi doesn't come with you when you enter the park. Yoshi is behind the Pianta shaped tree. Fruit is scattered around so unless you know where to look it may take a while to find the one needed to wake up the egg. Coconuts are in and under a tree next to the pirate ride. A papaya is hanging under the nose of the Pianta tree. A bunch of bananas is on the small ledge behind the pirate ride. A pineapple inside the gazebo. Finally, a durian is at the edge of the reflecting pool but is seldom, if ever, needed to wake up the egg.
Get Yoshi and hunt for butterflies on the beach to the left of the merry-go-round.