Here ya go!
That website is wrong in a few places.
In The Menagerie, Kirk's reaction to the mention of Lieutenant Helen Johansson's name implies at least a sexual hook-up, and not simply coffee.
In By Any Other Name, no we don't actually see it, but the impression I received is that Kirk was screwing Kelinda. Yes we only saw kissing.
In Elaan of Troyius, Kirk and Elaan were (in one scene) rolling around on her bed, that they're lovers is (again) implied.
Elaan: "Captain, that ancient Earth custom called spanking, what is it?"