When my paper was a biweekly, we did an April Fool's section. Clearly identified it as such. One story talked about a "robbery" at a Taco Bell in Podunk with an "artist's rendition of the suspect," which was a mugshot of my boss. Podunk police read the paper, had a good chuckle, then guffawed about people calling in saying they saw someone who looked like the "sketch."
Another story had our local three-sport star, who was a standout in football and baseball, opting to play basketball at Duke instead. He seemed to have a sense of humor about it.
It was good for a laugh, and people who actually looked at the "April Fool's Section" thought it was really funny.
We haven't done it since, a classic (and rare) case of quitting while ahead.