Webthe greene county jail project has been years in the making, as officials have long wanted to replace their aging jail on market street. Built in 1969, the facility. Webthe greene county jail has 1242 beds and an average daily population of 980 inmates. The facility supports the philosophy of modified supervision. This website contains booking photos of those persons currently incarcerated at the time you query this website. Information on this site is. Webso every inmate that comes through the doors makes the county’s and sheriff’s budget a little tighter. For almost 20 years, the city and county.