During the year of mourning is it permissible to sing to a child or yourself?
My apologies that it took so long to get back to you.
It is permitted to sign to oneself of a child while one is in the year of mourning, if the person is singing by themselves, and not together with a crowd. Also even an individual should not sing if it will bring him to actually dance, however it is not very common therefore in most instances it is permitted.
Halichos Shlomo Nissan-Av 14-3, Kovetz Halachos R’ S. Kaminetzsky Bein Hamitzarim 4- 5,6. Although they are referring to singing during the three weeks, the halachos of the three weeks are similar to the halachos of the year of aveilus.