For some reason, "funner" is a disfavored in what my linguistics professor used to call the "socio-economically preferred dialect", which is basically the educationally corrected language used by the socio-economic elite of society, at least in formal communication. This is a far cry from "funner" actually not being a word.
Is “funner” a word or not? [duplicate] - English Language & Usage ...
On the other hand, "funner" and "funnest" are not so unheard of that it has not made its way into some dictionaries, such as Merriam-Webster. If a word is in at least one major dictionary, it's safe to regard it as a word.
Who judges? "Funner" is, of course, a word in the same sense that "ponyfraggis" is a word, if "word" is defined as a pronounceable sequence of letters delimited by whitespace. In terms of usage, the frequency of use of "More fun" vs "funner" in formal writing suggest that "funner" is spoken slang. Naturally it is a word, too.
Fun is in reasonably common use as a adjective; but the comparative funner is rare, and some would say that it is not standard English. There is one instance of it in the Oxford English Dictionary, from 1996, "not one of the funner moments".
I think fun as an adjective is quite common. Merriam-Webster has a definition for this. It does state that "funner" and "funnest" are sometimes used but I, too, prefer "more fun" and "most fun". What adjective would you use if you wanted to eschew using "fun"? Any I can think of have slightly different meaning, e.g. "entertaining".