Absolute Boyfriend(2003)

Zettai Kareshi

Rejected way too many times by good-looking (and unattainable) guys, shy Riiko Izawa goes online and signs up for a free trial of a mysterious Nightly Lover "figure." The very next day a cute naked guy is delivered to her door, and he wants to be her boyfriend! Has Riiko died and gone to heaven? The cute guy turns out to be sweet, smart, a great cook, and lots more. And he looks like a million bucks, which is what he's going to cost Riiko if she doesn't return him in time...

(Source: Viz Media)

Included one-shots:
Volume 6: I Won't Let You Become a Star and Aromatic Boy