This is pretty self-explanatory. Basically, these shows in general, suffer from cliched, inconsistent, generic, or mediocre writing but were elevated by a likable cast with great chemistry.

hello larry worked imho because of the cast the writing was so so but the cast was great

Gilligan's Island

Designing Women. I quote lines from it all the time, so I wouldn't say the writing was bad; but some of it was cliched (and now very dated). Dixie, Delta, Annie, and Jean were perfectly cast and managed to make the political and message-y stuff from the Thomasons palatable.

The Beverly Hillbillies.

Married...With Children has to be up there near the top. The writing was pretty good in the early years. The last few seasons the writing was horrible, but all the actors had their characters down pat, so the show was still successful.

hello larry worked imho because of the cast the writing was so so but the cast was great

I would agree, but the show didn't actually work. I like it, but it was cancled after only 38 episodes.

I agree that Gilligan's Island, I Dream Of Jeannie, and Beverly Hillbillies have a stronger core of actors compared to the writing. I Dream Of Jeannie had fairly decent writing in it's 1st season but then the series switched to color episodes in season 2, and by the 3rd, 4th, and 5th seasons some episodes are nothing more than a nonsensical farce.

I suppose the opposite question can also be asked: Are there sitcoms that have great writing but with a lackluster core of actors?

Buck Rogers in the 25th Century.