In order of what I think fits best, one being that it fits really well. Not necessarily in the order of what I think is the best manga. First three are must-reads.
1) "Kamisama ga Uso wo Tsuku." reminds me a lot of Koe no Kotachi."
2) "Satougashi no Dangan wa Uchinukenai: A Lollypop or A Bullet" is very "Your Lie in April," but darker. I will never forget this story.
3) http://www.mangago.me/read-manga/tetsugaku_letra/ is brilliant, imo. Fits the criteria pretty well.
4) http://www.mangago.me/read-manga/doukyuusei_nakamura_asumiko/ and its sequels. Much lighter, but still with its drama.
5) http://www.mangago.me/read-manga/aku_no_hana/ is VERY dark, but absolutely AMAZING. It gets much happier towards the end, though.
6) http://www.mangago.me/read-manga/hyakuman_tsubu_no_namida/ is supernatural, but definitely fits, imo.
7) http://www.mangago.me/read-manga/udagawachou_de_mattete_yo/ is about coming to terms with sexuality
8) http://www.mangago.me/read-manga/can_t_see_can_t_hear_but_love/ isn't really coming-of-age, but definitely about what it means to be alive.
9) http://www.mangago.me/read-manga/bokutachi_futari_ga_koisuru_riyuu/ fits.
10) http://www.mangago.me/read-manga/sannin_gurashi/
http://www.mangago.me/read-manga/haru_no_houtai_shoujo/, while supernatural, gives that kind of feel. Might be a long shot, though.
11) http://www.mangago.me/read-manga/inari_konkon_koi_iroha/ might be pushing it, but it definitely gives off coming-of-age to me, though the mood is a lot different than the series you mentioned.
12) "Sennen no Yuki" is really pushing it, but I felt it was worth adding.
Omg how could I have possibly forgotten?!
http://www.mangago.me/read-manga/kouya_no_koi/
This would probably go at #2, if not #1.
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I LOVE slice of life manga that's all about coming of age and exploring what it means to be alive. And if there's a bit of romance thrown in there too, that's perfect! Manga like Koe to Katachi (A Silent Voice), Hourou Musuko (Wondering Sun), and even Your Lie In April. Any suggestions?