At which age should children be trained not to listen to music during sefira.
Rabbi Simchah Bunim Cohen in "Children in Halachah" (Artscroll, page 186) places the age at seven or eight, although he is technically speaking about the three weeks (I don't think there is any reason which would make these two periods different).
ספר שמע בני by Rabbi Dovid Weinberger, also speaking about the three weeks, says that children who have reached chinuch should not listen to music during the three weeks (page 69).
Indeed Rabbi Cohen above also said that the age was "chinuch but gave a more specific age while Rabbi Weinberger discusses the difference of opinions about the age of "chinuch in the beggining of his sefer (page 10-11).
Incidentally Rabbi Cohen cites the Igros Moshe O.C. 4:24d while Rabbi Weinberger cites Igros Moshe O.C. 4:21d. It seems likely that one of these is a typographical error and when/if I have a chance to look further I will, bli neder, try to clarify.
I have heard in the name of Rabbi Yitzchok Breitowitz that you may listen to kids music with your small children during sefira if you wouldn't listen to it by yourself (the vast majority of the stuff little kids seem to like). Perhaps a corollary is that by the time they start listening to decent music, it is time for them to stop during sefira.