Depends on what you would define a frog's 'happiness'.
They seem to be happy enough in a 10 gallon if you have only one frog.
As long as they have plenty of food and clean water, he'll turn into a fat slob in about a year. Mine lives in a colony of 5, 2 males and 3 females.
They get the run of the small, enclosed backyard we have whenever their terrarium is being cleaned. They don't seem to want to go anywhere though.