I'm looking for yaoi mangas that show the couple's life together. Most romance mangas (yaoi, shounen-ai, shoujo, etc) just show the getting-together/falling-in-love part of the relationship, not the part that comes afterward: how they share their lives together, the trials they go through being gay, etc.

An example of this (and it's they only one I can think of right now) is Haru wo Daite Ita by Nitta Youka. I don't really care for the first few volumes of this yaoi (because the main characters are porn stars) but the rest of it is really good and exactly what I'm looking for.

I don't care too much about the art, so long as it's not horrible or hard to understand. Oh, it would also be nice if the story was 2 or more volumes long, but that's not necessary.

Have not read that one. Will solely base my recommendations on yaois that have couples living together and their lives after the whole "getting together crap". Some have to do with trials based on rejection and whatnot...

LIVES TOGETHER~
Akai Koi--What you're looking for. Try more of the mangaka''s works as well.
Shitsuren Mania--What you're looking for, quite a good read too.
Zoku Kagakushitsu e Douzo--More like the second pairing...meh, kinda.
Bed no Ue no Tengoku--Not really after, since they don't get together until chapters later. But it does go through the whole "life of two man in love and under the same household..."
Darenimo Aisarenai--Highly recommended. More or less what you're looking for. Also try some of the mangaka's work.
Wonderful Life--A fav. A good read, but the couple is already together, don't know if you mind that or not.
Aishiteru--Also a fav. But again, the couple is already together.
Kanga ne Spoon--Again, couple already together. :/

TRIALS~
Ano Kado wo Magatta Tokoro--More or less there are trials other than the whole "fall in love" plot.
Okujou Fuukei--A highly recommend this one, not sure whether it fits or not though.
Cut--Also a good one, a few trials here and there.
Complex--Highly recommended. It's a story about their whole life! What's not to love?
Ai no Kotodama--A really good read. Trials after getting together, a bit of rejection...
Junjou Romantica--Hate myself for recommending this one! Only doing it for the second pairing, becuase it fits what you're looking for. The third pairing as well.
Love Mode--Has couples left and right. Main pairing is somewhat as you describe.
Koi ga Bokura wo Yurusu Hani--Highly recommended. Definitely what you're looking for. Enough said.
Dear Green--Recommended. There are trials...but they are already together. I think the sequel/prequel deals more with that though.
Yatteraneeze!-- Many trials, even rejection of sexuality. Mixed about this one, but well, it meets your criteria.
Little Butterfly--Trials...angsty. But still a fav.
Yellow--Odd recommendation...they are together, but their "trials" are somewhat different. Read the summary to get an idea.

Hope you find something you may like~^-^

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I really like these types of yaoi too. Any new suggestions?

A Bus To Hell - the first volume only. The couple is already together, and it shows how despite their opposite mentalities, that they still love each other. Second volume is a totally different story.

Sorenari ni Shinken nandesu - They do start "living" together after a couple of a chapters.

Yachin Hanbun no Ibasho desu - Ch 1-3 seems to fit.

The Cornered Mouse Dreams of Cheese & The Carp on the Chopping Block Jumps Twice - The first one shows how they get together, and the second one deals with them living together, and other dramatic happenings. And boy are they dramatic.

I don't know if you only want scanlated manga, but Kumota Haruko's Itoshi no Nekokke is about a gay couple who start living together after a long time apart and all the problems they encounter in their relationship. It's very cute.

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Yeah I only read scanlated manga, but thanks for the suggestion