sort of laugh? I cant think of what it's called. It's when you are sort of staring into space, and someone makes a light joke to try and cheer you up and you sort of let a gust of air out rather than a laugh, as if to say 'Thanks for trying but I'm really upset'. It's a really difficult question but thanks for the time 
I can see this isn't a very good explanation. I'm not thinking of someone who is bitter or anything. This is the context: “Good afternoon darling” I joked. Her eyes stayed fixated on the wall, but she just *insert word*; it was her best attempt at a laugh.
This woman is upset because her son has died, her eyes are fixated on the wall and her thoughts are in another place. She's not being sarcastic, she's upset and can't really feel the laughter.
I can see this isn't a very good explanation. I'm not thinking of someone who is bitter or anything. This is the context: “Good afternoon darling” I joked. Her eyes stayed fixated on the wall, but she just *insert word*; it was her best attempt at a laugh.
This woman is upset because her son has died, her eyes are fixated on the wall and her thoughts are in another place. She's not being sarcastic, she's upset and can't really feel the laughter.