A new State Planning Council to be headed by Democratic Gov. Richard W. Riley of South Carolina was appointed yesterday by President Carter to counsel the federal government on the suitability of nuclear waste disposal sites.

The council's "purpose is to advise the executive branch and work with the Congress in finding better ways to address radioactive waste management issues," Carter said in a message sent to Congress yesterday, "such as planning and siting, construction and operation of facilities. Legislation will be submitted during this session to make the council permanent."

Besides South Carolina's Riley, Carter appointed seven other governors to the council. They are Democrats John V. Evans of Idaho, Ella Grasso of Connecticut, Harry R. Hughes of Maryland, Bruce King of New Mexico and Dixy Lee Ray of Washington, and Republicans John N. Dalton of Virginia and Robert List of Nevada.

Named vice chairman of the council was Paul Hess, a state senator from Kansas where the federal government tried to establish the nation's first nuclear refuse dump almost 10 years ago.

Others appointed to the council were Stanley Fink, speaker of the New York State Assembly; Gordon Voss, a state representative from Minnesota; Ernest Morial, mayor of New Orleans; Mary Louise Symon, chairman of the Dane County, Wis., board of directors, and Peter MacDonald, chairman of the Navajo Nation of New Mexico.

Most council members are from states that could play role in President Carter's new plan to dispose of nuclear garbage. Among the sites identified as possible burial grounds for radioactive waste are locations in Washington, Nevada and New Mexico. Sites identified as candidates for storage of spent fuel are in South Carlina and New York.