I have one sort of along the line of that. http://www.mangago.zone/read-manga/romantic_joutou/
No, the omega mate with the alpha out of frustration i think. I cant remember much. But the one you suggest is a good one tho. Just finished it. (￣∇￣")
The alpha have a black hair, soft spoken and rich , age group i cant remember, the beta live in an apartment alone. After the alpha and omega mate , the omega to the beta apartment during rain and crying and show the bite mark to the beta. That all i can remember . Sorry not much.
What i can remember is the alpha looks like anime character kaname kuran in vampire knight the beta have a shoulder length white or blond hair i think. The art is good i mean like its like katekyo I read it in this site. The art like katekyo! Its more recent manga. Thats all i can remember. I wish i can remember more. （/TДT)/
The omega is your typical omega , small , cute with angelic face, big round eyes and black hair if im not mistaken.
This omega in love with the seme (i think a beta) then being push away by the seme. The omega go to an alpha who so invested to him and they mate. After that the omega went to meet the seme again. When i was reading the manga it still ongoing but i cant recall the manga. Please help me. Thanks in advance tho.