I think "Spectre of the Gun" could be said to have some funny moments, especially with Chekhov, and the whole "fish out of water" aspect of our heroes in this weird Melkotion trap. And "Day of the Dove" ends lightheartedly and with some humor, at least (Kang slapping Kirk very hard on the back).
But the backslappery at the end of "Day of the Dove" was forced: They had to behave that way to eject the alien from the ship. As for "Spectre," to me it was more weird than amusing; the only characters that seemed to be having fun were the illusory Earps and Doc ("Your emergency sure is real!"). However, there's some fun to be had in the music by Jerry Fielding - such as the bitonality (each hand playing in a different key) of the honky-tonk piano in the saloon scene.
(I saw both on NBC as a pre-teen.)