"Make someone happy" is far and away the most common thing to say. I can see a situation in which you say to someone "Let's go out and see if we can get you happy again" but it's NOT common.
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PieanneI think "he made me angry" is the most frequent expression, though "he got me angry" is more used than "he got me happy"And I, as a native speaker, have absolutely no idea why that is true, but it is. Just one of the joys of learning English