Opposite is: not serious

1. My big dictionary DOES have the adjective "nonserious." 2. But I think that many native speakers would express the same idea by using other words: The president: OK, ladies and gentlemen. I am ready to answer your questions. Reporter: What is your favorite ice cream flavor? The president: I'm very sorry. But I am not going to answer a FRIVOLOUS question like that. (frivolous = not serious) ***** In the 1990's, a man was running for president of the United States. Someone asked him what kind of underwear he wore. He answered the question! Many people said that a candidate for president should not answer such a frivolous -- and impertinent -- question! (impertinent = not showing respect)

"Unserious" and "non-serious" are both valid words, though situationally and rarely used. A native speaker would rather use "not serious" or an antonym like "funny", "light", "trivial', etc.