Coin 1: In the upper left of the racetrack/marathon. Coin 2: In the invisible room. Jump up the visible platforms and go straight right. Coin 3: Under the white portal above the Pink Zone. Jump into the other white portal above the typing area to nab it. Coin 4: On the striped platform. Complete the invisible maze and go through the yellow portal to get it. Coin 5: In the Green Play Room. Coin 6: In the air for you to get after jumping off the blue star. Coin 7: In the Pink Zone. Coin 8: On the first floor of the building to the left, in the window. Coin 9: In the observatory/floating room/big black room at the top. Jump up a few platforms to be able to reach it. Coin 10: Near the jail. You can jump off the No button to get it.

No, I don't know why they're numbered this way either.

EDIT: There is a map on the Discord server in #about