A yaoi manga where one of the characters, (he doesn't have to be the main character) is really cute but very serious.
Is it possible that there is a manga where the overly serious person is clumsy? (this can be non yaoi too)

There's no I in TEAM but there's a U in SUCK

No Color

Obsession is a drop of water in the desert- crave it, savor it, remember it. ~Unknown

This kinda made me think of Lucky Number 13 by YAMAMOTO Kotetsuko. The main guy tends to have a serious-type air about him, but has a very cute side (unless it's just me who thinks that?).

I believe it was licensed though, so Bliss may not scanlate the second volume. -_-;

I would say Shio from Merry Checker. Because he is so precious * --* and i guess the character from Bukiyou na Silent? though he's more expressionless than serious.