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The meaning is clear; however, I'd change it anyway to make it a stronger sentence. Try, "The happiest time of my life".

Its so idiomatic that hardcore prescriptive grammar rules are almost irrelevant here. Then it just becomes a question of meaning, tone, audience, etc.
And by the way, you ARE saying that the times were happy (for you).

It's fine as posted. The second post in this thread offers a phrase with a slightly different meaning--was it the happiest time of your life or just one of the happiest times of your life ?