Really good singers are in high demand, so be sure to book yours well in advance. In most circumstances, 3-4 weeks should be sufficient; but if you're looking for a singer at a holiday event, you'll need to have your bid in as much as several months earlier.
If you're looking to hire a country singer, check around your town for a local Opry, in the tradition of Nashville's Grand Old Opry. Often, small towns (especially in the South) have venues that foster local talent. For example, superstar LeeAnne Rimes started out at the tiny Garland Opry in Garland, Texas.