Filimonas shows how to get all 63 coins in this video. My comments from when I didn't think this was possible are shown below...

My best coin score for this level is 53, although I now think that 54 coins is possible as well. You can use as many Wing Caps as you want, but you must get all the coins in one run through. Getting 53 coins is probably the best test of flying skills in the entire game. My method of doing this is to get every coin in the coin trail, and fly through the first two rings getting both red coins, and three (yes, three) of the yellow coins. This takes very precise flying skills, and maybe a little luck too. For the third ring, get as many coins as you can when you first fly through it, then get the next 1 or 2 coins in the coin trail, then turn around and get the rest of the coins from the third ring... You can get another two passes through the ring. Finally, quickly fly above the tower, because your Wing Cap is about to run out. You should have 39 or 40 coins now. The remaining 13 coins can be obtained from the Wing Cap on the tower. If you're really good at flying, you might be able to get the second last coin from the coin trail, so you could get a maximum of 14 coins just from the tower. Good luck! To my knowledge I'm the only one who has ever gotten 53 coins here. (Then again I may be the only one who wasted my time trying to do it.)