The only successful sitcom that aired on CBS in the early to mid 80s that I can think of, was Kate & Allie.
When I think of sitcoms and the 1980s, I am more likely to think of peak Diff’rent Strokes, peak Facts Of Life, and the start of NBC’s ‘Must See TV” Thursday night lineup, and Who’s The Boss?, Webster, Mr. Belvedere and the early beginnings of ABC’s TGIF lineup. Even Fox was starting to compete by the end of the decade and with syndicated television shows like Small Wonder (which got heavily made fun of by other student writers in my grad school sitcom class but even they had to admit to having watched the series as little kids-we all had to) and What’s Happening Now that aired on my local Fox broadcast network, Fox was starting to embed in the weekend time slots as early as 1985.
CBS was fortunate to get any traction from their sitcoms that were 70s holdovers exiting the television landscape in the 80s. Other than Kate and Allie, the only other memorable sitcom in that era was Charlie & Co., which CBS ultimately badly flopped by changing its time slot just as it was starting to cultivate an audience and throwing the nascent sitcom into the lions den of direct competition with 80s powerhouse The Cosby Show, which just seems cruel, in retrospect.
I agree with @Paul Ravenabout CBS’ sitcom programming cupboard almost being completely bare by the mid 80s and it was pretty much their own poor choices that led them there.