My birthday is on the 29th. I even requested the song and he says he only plays it on special occasions. I thought K.K. played the song for you the weekend before your birthday?
Yep KK will come on your birthday to play the song! If any friends come to your island before then and sees KK, I think they can request birthday notes to be shown to you during your bday song.
I can confirm this. My birthday was on the 18th of this month. He came in to play that song. (It was Friday when he came.) Afterward, I saw him again the next day.