King tried to come back from a hamstring injury last week but returned to the sideline Wednesday after a setback.
He has played only 15 games since the Packers made him a second-round choice in 2017. King ended last season on injured reserve, too.
Carson has a rib injury. He played four games after the Packers promoted him from the practice squad Oct. 31.
Green Bay needed the roster spots for two waiver claims.
Jamerson appeared in 10 games for Houston, making seven tackles.
Brown played eight games for Oakland this season and made 17 tackles and a pass breakup.