Mangas

I Hate My Girlfriend's Bias -  彼女の推しがきらい -  推しきら
The troubles of the handsome college student, Kei Tachibana, is that his cute, older girlfriend, Chisa, is crazy about other men. What's more is that the men are 2D "Oshi Characters." What tomorrow will Kei-kun face as he fights against those blasted "Oshi"? This is a love comedy between a younger, devoted boy and working otaku girl!
Tsukako in the Death or Marriage -  Tsukako's Marriage Hunting Death Game -  ツカ子の婚活デスゲーム
28 year old otaku Suzuki Tsukako visits a marriage consulting office, but the counselor there is a shinigami who forces a contract on her and tells her that if she can't get married in a year she'll die. Because of her selfish and ill-natured personality combined with her lack of experience in relationships and the arrogant view that she'll be able to effortlessly find the dream partner without spending the time or money, the system calculates that her chance of success is 0.03%. So that she can live to see the future of her favorite 2d idol group, she accepts the challenge. (Source: Mangaupdates)