Produced between the first two movies in the series, Men in Black transitioned to an animated series, airing on Kids' WB! from 1997-2001, with reruns airing briefly on Nickelodeon. Since Sony owns the rights, they likely have the series locked in the vaults at present, as it wasn't re-released to coincide with "Men in Black 3" several months back.
The roots of MiB start with an independent comics series created by Lowell Cunningham for Aircel Comics, which along with sister company Malibu was bought out by Marvel, and that explains why the movies claim that the series actually began at Marvel, which it certainly didn't.
While it was highly unlikely that stars Will Smith & Tommy Lee Jones would reprise as Agents J & K, respectively, in the cartoon, the producers did their best to compensate, though they would end up with 2 actors playing K. Ed O'Ross was hired initially, but was replaced by Gregg Berger (Duckman) in season 2. Jennifer Lien (Star Trek: Voyager) stepped in for Linda Fiorentino as Agent L for the first 3 seasons, but left the show, due likely to conflicts with her Voyager commitments. Only two cast members from the movie crossed into the cartoon. Vincent D'Onofrio not only reprised as Edgar from the film, but also his twin brother Edwin, who came seeking revenge for Edgar's death. Tony Shalhoub (Monk, ex-Wings) played the Deeks brothers at first, but due to Monk, left the show and was replaced by Billy West (Futurama).
Here's the open, taken from a Nick broadcast: