There's got to be a better way...

build.sbt

// Don't include private.conf in main package.
mappings in (Compile, packageBin) ~= {
  _ filter {
    case (_, "private.conf") => false
    case _ => true
  }
}

// Don't include private.conf in main sources package.
mappings in (Compile, packageSrc) ~= {
  _ filter {
    case (_, "private.conf") => false
    case _ => true
  }
}

// Don't include private.conf in test package.
mappings in (Test, packageBin) ~= {
  _ filter {
    case (_, "private.conf") => false
    case _ => true
  }
}

// Don't include private.conf in test sources package.
mappings in (Test, packageSrc) ~= {
  _ filter {
    case (_, "private.conf") => false
    case _ => true
  }
}