Reading up on it more, I don’t think cherries are a significant source of melatonin. Montmorency cherries have about 13.5 nanograms (billionths of a gram) in one gram of fruit flesh, so you would need to eat about 60 kg of fresh pitted cherries to get one milligram of melatonin.
By comparison, IIRC, pistachio nuts (dried, no shell) have about 6.6 mg melatonin per oz or about 1/4 mg melatonin per gram. Thus you would need to eat about 4 grams of pistachio to get one milligram of melatonin.
IF tart cherries help people get to sleep, it can’t just be the melatonin. By the way, Rainier cherries have about six times as much melatonin as Montmorency cherries — still not a significant source. You would only need to eat 10 kg of Rainier cherries to get 1 mg of melatonin.
(The last sentence ended up in the wrong paragraph when first posted.)
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I stole this post and put it on Telegram NIATONIN channel. They are discussing cherries.