It depends on whether you think "fun" is an adjective.
"Fun," the Inflected Adjective
And here's where it gets really contentious. This is where I got stuck looking up reference after reference trying to find a convincing answer. If people accept that “fun” is an adjective, they should accept that “fun” can be inflected like other adjectives. If “crazy” becomes “crazier” and “craziest,” and “silly” becomes “sillier” and “silliest,” why can't “fun” become “funner” and “funnest”?
In the episode on comparatives and superlatives, we told you that "one-syllable adjectives use the suffixes ‘-er’ or ‘-est’ on the end of the adjective. For example, ‘tall’ has one syllable, so, if you wanted to compare the height of your family members, you might say, ‘I am taller than my sister, but I’m not the tallest in the family.’” If you accept that "fun" is an adjective, the way to compare the funness of two or three things would be to use the words "funner" and "funnest."
Yet, even people who accept that "fun" is an adjective are unlikely to embrace "funner" and "funnest." It seems as if language mavens haven't truly gotten over their irritation that “fun” has become an adjective, and they've decided to dig in their heels against “funner” and “funnest.” In their minds, if “fun” as an adjective is still informal, then the inflected forms are still “nonstandard,” or to use less fussy words—“funnest” is grating and horrifying. And the language mavens still have enough influence to hold the line for now.
However, it’s probably a losing battle. Again a Google Ngram search shows a big and ongoing increase in the use of “funner” and “funnest” in books starting around 1980.
Next: The "Fun" Continuum