Dr. Bernice King tells TMZ ... the recent firing of Rochester, NY weatherman Jeremy Kappell went too far. If you haven't seen it, Kappell referred to a park named for MLK ... "Martin Luther Coon King Jr. Park" while he was on air last week.

Shocking, but still ... Bernice believes there's a better way to handle the situation than 86ing the guy.

Bernice says, in this instance, Kappell's racial slur seems to be a one-time flub ... so the station should have cut him some slack. She agrees there needs to be repercussions -- along with an apology -- but suggests it doesn't do anyone any good to just fire the guy.

She told us what she think the better course of action would have been.

As for Kappell, he issued a public apology with his wife on Facebook, insisting he accidentally jumbled his words and didn't do it with malice. He also criticized the TV station for letting him go and not supporting him, adding ... "I would never intend harm that way to anyone."

Speaking of intent, we asked Bernice about that too, and she tells us someone who says "coon" publicly has probably heard it frequently in private or even said it in the past, which is why rehabilitation is so important.

And, for what it's worth -- maybe the most famous meteorologist, Al Roker, is on Jeremy's side.