Staying with your cousin is one thing; however, things can happen in this Yaoi Manga Recommendation.
Today’s Yaoi Addiction Society’s Yaoi Manga of The day is Takaramono
Naoyuki, a sincere and honest country boy comes to Tokyo for high school and stays with his cousin’s family. At first everybody takes advantage of him, thinking that he’s too naive to catch on. His cousin Satoshi, who’s in college, is no different. He demands that Naoyuki have sex with him in exchange for tutoring him… In no time, despite his less than honourable initiate intention, Satoshi starts falling in love with the pure-hearted boy.
2) Kimochi no Yukue
Oneshot also found in Double Lover – Koibito no Namae.
Futuristic Sci-fi story about a singer and an android that was abandoned. Not scanlated.
2) Kimi to Konomama
Tells of a tragic love story between a boxer with an incurable illness and his loyal fan. Not scanlated.
3) Takaramono EX
2) Kimi ni Ai ni
An exchange student from Britain suddenly proclaims his love for his Japanese classmate and goes on the offence. Oneshot also found in Saikou no Kimi.
AKA Promise, also found in Koibito no Jikan.
Summary from https://www.mangaupdates.com/series.html?id=597