The phrase "almost as happy" is correct and usable in written English.
It can be used to compare levels of happiness between two subjects, indicating that one is nearly as happy as the other.
Example: "After receiving the good news, she was almost as happy as her best friend who had just won the lottery."
Alternatives: "nearly as joyful" or "close to as content".
He was almost as happy about that accomplishment as winning the Stanley Cup.
Sutherland was almost as happy for DeGale in Beijing as if he'd won the major prize himself.
Someone suggested to Williams later that she looked almost as happy as Kerber during the trophy presentation.
But it's gouging if you'd be almost as happy paying less than half as much for discounted seats to, say, "Anything Goes".
An excellent linguist, he was almost as happy singing in Italian, French and English as in his native tongue, and he spoke English with virtually no accent.
A lawyer for Gov. George W. Bush said, "I'm almost as happy that it's just over as I am that we won".
In order to evaluate the level of happiness, pollsters interviewed 55,817 men and women who responded to the question: "As far as you are concerned, do you personally feel happy, unhappy or neither happy nor unhappy about your life?" The survey found that Colombians are almost twice as happy as the global average.
The relationships between people are satirical, almost as if happy, well settled people were being made fun of.
Then, when the scoreboard goes up, she shares the moment with her UCLA teammates, who have been mirroring her dance moves from the sidelines, and seem almost as deliriously happy as she is.
Kay, who it turns out can lip-read, almost passes as happy with my progress.
Má Pêche, Bar Boulud and other glossy restaurants have become almost as infusion-happy as the less mainstream bars and lounges that beat them to the punch.
