I've been looking for a certain song since yesterday, and I can't find it. It played at the last episode (12) of the second season of Sekaiichi Hatsukoi; it's at the part where Masamune sat on a bench at a subway station, and he held Ritsu's hand. The song started at 21:39, and it played before Aikotoba (the ending song).
Deleted previous answer. You can always look at the edit history if you want to see it again. :)
Is this the scene when the piano bit plays for a while? If it is then it is actually part of the ending song.
I am not too sure why they decided to play it at that moment before the ending song but I am fairly certain it's part of the ending song.
FYI ;): If you listen really closely, that same tune is actually part of the ending song (Aikotoba) itself at 1:27 (it's actually part of the ending song).