Kai does have a blue heart event. o.o
Have you gone to the beach between 2:30 and 5:00 pm? And make sure that it's a sunny day when you go. Those are really the only requirements for Kai's heart event.
But from what I read, isn't it good to have a green heart? It gets them that much closer to yellow, to orange, to red, so...?
If you do need any further help, just head to gamefaqs.com and search for "Harvest Moon DS Cute". Then go to the Marriage FAQ. I would link you, but Gamefaqs doesn't allow links.
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