Like a few of the others, I'm not sure entirely what you mean by “change their sound.” WINC has been on multiple signals during the course of its existence. So, it wouldn’t seem to fit that bill, or at least it wouldn’t to me.
In your neck of the woods, KSYN 92.5 has always been top-40. I don’t know, however, that it fits the definition of not having ever changed its sound. In its final couple years under William B. Neal, it aired ABC/SMN's “The Heat“ part-time, and it kept the satellite programming after “The Heat” switched to Hot AC. I'm not sure if it kept the CHR sound or adopted the Hot AC logs during that time when it ran local programming. Mr. Neal, by the way, was an interesting character. He ran those radio stations for a long time but never really got on board with FM. He always thought it was a passing fad. Chuck Dunaway used to walk his dog past the station on an almost daily basis, and the two became decent friends. Mr. Neal was more than happy to swap KSYN to Dunaway for WMBH and cash because he still thought AM was where the money was.
KIXQ, far as I know, has always been country, but it started at 93.9 and merged with the former KJKT ”Country KAT 102.5” in 1997.
KBXR in Columbia has always been a AAA, but it started at 106.1 and moved to 102.3 after 4-5 years.
Many of the ex-Shepherd country stations have had the same sound for decades, but a few of them moved from AM to FM in the late 70’s/early 80’s. KJEL was about the last one to move, going from 750 to 103.7 in the early 90’s.
KMZU in Carrollton, MO has changed very little during its lifespan, but it was moved to 100.7 from 101.1 to accommodate the reverse move of KCFX when it moved to I-435 and I-70 near the Truman Sports Complex around 1990-91.