Shin Dousei Jidai: Hawaiian Breeze

In this adaptation of a manga by Fumi Shibama, itself a retelling of a 1972 manga by Kazuo Kamimura (the original Age of Cohabitation whose existence is implied by the "new" in this title), Honda has been living with Eri for two years and debates whether or not he should ask her to marry him. (Source: The Anime Encyclopedia)