Brentwood-based Diversicare Healthcare Services Inc. is adding another Kentucky facility to its roster, the company announced Wednesday. The company has assumed operations of a 62-bed skilled-nursing center in Greenville, Ky., which will be rebranded as Diversicare of Greenville. The facility is expected to contribute $4.5 million in revenue annually, according to a news release. "We are pleased to announce our latest expansion to our current operating footprint in the state of Kentucky," CEO…