Before the Addams Family TV show from the 1960s and the Addams Family films from the 1990s, there were the cartoons by Charles Addams. They primarily appeared in the New Yorker.
Most of the characters from the TV show appear in the cartoons. Thing and Cousin It were not in the cartoons as far as I know but every other major character was in the cartoons. Addams also drew other cartoons that featured his sinister sense of humor. Books and prints are available. This is the link to the Tee and Charles Addams Foundation.