"particularly happy" is correct and usable in written English. You can use it when you want to emphasize the degree of happiness that someone feels or to describe something as being unusually happy or joyful. For example, "The children were particularly happy to receive presents on their birthday."
He didn't sound particularly happy.
Theirs was not a particularly happy union.
He doesn't look particularly happy.
Nobody seems particularly happy or unhappy.
"I am particularly happy for the family.
"We're not particularly happy with this stone".
It will not be a particularly happy gathering.
Humbletonian does not look particularly happy to see her.
None of us were particularly happy in law school.
However, Sadiq isn't particularly happy to be trending nationwide.
Italy's parish priests are particularly happy with him.
I love the desktop app, it’s always running on my Mac. Ludwig is the best English buddy, it answers my 100 queries per day and stays cool.
Cristina Valenza
Retail Lead Linguist @ Apple Inc.