He'd be pro-life, pro-traditional marriage, noninterventionist foreign policy (which is the true center-right foreign policy). His niece Alveda had said so on many occasions.
Assuming this is true, that still doesn't count for the main unifying point of the GOP and the main unifying point of Conservatism, regardless of whether it is between Libertarians or socially conservative hawks: Economic and Fiscal Conservatism. I doubt King would be in favor of kicking poor African-Americans off their welfare. In fact, I remember an article where he believed an even better program would be warranted to help make up for the centuries of enslavement. Beliefs like that don't tend to sit well with the Centre-Right.