Where in the canon does the Buddha say, There is no happiness without calm?
I've heard the statement only second hand, and paraphrased.
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"There’s no fire like passion, no loss like anger, no pain like the aggregates, no ease other than peace."
~ Dhammapada 202, transl. Thanissaro https://www.dhammatalks.org/suttas/KN/Dhp/Ch15.html
It's the other way round according to Kimattha Sutta.
Without joy, you cannot have serenity.
Without serenity, you cannot have concentration.
Without concentration, you cannot become liberated i.e. attain Nibbana.
Dhammapada 204 says that Nibbana is the highest bliss. And without serenity, you cannot attain the highest bliss. So the other way round is also explainable.
"Thus in this way, Ananda, skillful virtues have freedom from remorse as their purpose, freedom from remorse as their reward. Freedom from remorse has joy as its purpose, joy as its reward. Joy has rapture as its purpose, rapture as its reward. Rapture has serenity as its purpose, serenity as its reward. Serenity has pleasure as its purpose, pleasure as its reward. Pleasure has concentration as its purpose, concentration as its reward. Concentration has knowledge & vision of things as they actually are as its purpose, knowledge & vision of things as they actually are as its reward. Knowledge & vision of things as they actually are has disenchantment as its purpose, disenchantment as its reward. Disenchantment has dispassion as its purpose, dispassion as its reward. Dispassion has knowledge & vision of release as its purpose, knowledge & vision of release as its reward.
"In this way, Ananda, skillful virtues lead step-by-step to the consummation of arahantship."
Kimattha Sutta (Ven. Thanissaro's translation)
The Pali terms used:
Please see here for Pali-English translation based on Ven. Sujato's translation.