http://www.mangago.me/read-manga/kimi_no_kanaderu_hikari/
http://www.mangago.me/read-manga/pure_dakkang/
http://www.mangago.me/read-manga/bokutachi_futari_ga_koisuru_riyuu/
http://www.mangago.me/read-manga/inu_to_tsubame/
http://www.mangago.me/read-manga/eien_no_aida_ni_miru_yume/
http://www.mangago.me/read-manga/pokerface_lee_ki_ha/
http://www.mangago.me/read-manga/birthday/
http://www.mangago.me/read-manga/machina_angelus/
This is a new one and based on the first chapter ur sure to be crying http://www.mangago.me/read-manga/ashita_shinu/
These have made me cry...Some take a while but nonetheless they've pried salty water of pain from my eyes.
http://www.mangago.me/read-manga/usemono_yado/
http://www.mangago.me/read-manga/tomoi/
http://www.mangago.me/read-manga/berserk/
http://www.mangago.me/read-manga/heads/
http://www.mangago.me/read-manga/battle_royale/
http://www.mangago.me/read-manga/zankoku_na_kami_ga_shihai_suru/
These do come under the genre of romance or shoujo and have female characters, but i don't consider them annoying. And rather than purely focusing on the intimate aspects of relationships it focuses on the individual and their dilemmas. (i've cried to all of these)
http://www.mangago.me/read-manga/deep_love_ayu_no_monogatari/
http://www.mangago.me/read-manga/watashitachi_no_shiawase_na_jikan/
http://www.mangago.me/read-manga/hwaja/
http://www.mangago.me/read-manga/life/
These give off a sad and existential feel, crying is optional.
http://www.mangago.me/read-manga/kanai_kun/
http://www.mangago.me/read-manga/sekai_no_owari_to_yoakemae/
I need manga that could make you cry. I just have a shitty days and need to let off some steam. Problem is, it's hard for me to cry, like, really hard. I can't cry if the sad things are about someone who involved with the other romantically (no romance), but I can cry if it's about families. Like kono oto tomare, or donten ni warau, that's the kind of manga that could makes me cry. So, can you recommended me something like that? if possible, no annoying female character. Thank you