"less unhappy" is correct and usable in written English.
You can use it when comparing two or more levels of unhappiness. For example, "He was less unhappy after he talked to his friend."
Yesterday, he sounded calmer, although no less unhappy.
And, despite its problems in Gaza, Hamas looks the less unhappy of the two.
It does not attract happy people, nor does it make its unhappy practitioners any less unhappy.
It won't make everyone happy, but at least it should make some people a bit less unhappy.
Mason said: "I was more or less unhappy about the trade when I heard I was going.
Indeed, Alistair's semblance of a life appeared to be no less unhappy for all his ability to articulate its pain.
Fewer hiring mistakes also lead to less frequent unhappy firings.
But another, in the Guardian, was less impressed, unhappy with its "awkward dialogue, pedestrian prose and depressingly cliched situations..
Her style is so self-assured and strongly personal that it is hard to believe her singing career was an accident -- much less an unhappy one.
Although people who describe themselves as happy enjoy watching television, it turns out to be the single activity they engage in less often than unhappy people, said John Robinson, a professor of sociology at the University of Maryland and the author of the study, which appeared in the journal Social Indicators Research.
Recent research says these offices make us sick, less productive and unhappy.
