I'd prefer to stay away from The Unfunny territory. The character I have in mind likes cracking jokes along with a friendly smile but the situation she is in keeps trying to push her into a grim mood. But she's no Stepford Smiler as she's grateful for the good things she has in her life.
The big thing about Stoics is that they display no
emotion, positive or negative. You just described a character who is some variation of The Pollyanna
. However, a character who cracks jokes with a straight face and no visible emotions and is also grateful for the good things in her life would be a Stoic