MyAutofacActivator.cs

public class MyAutofacActivator : JobActivator
{
    private readonly ILifetimeScope _lifetimeScope;

    public MyAutofacActivator(ILifetimeScope lifetimeScope)
    {
        _lifetimeScope = lifetimeScope;
    }

    public override JobActivatorScope BeginScope(JobActivatorContext context)
    {
        var connection = context.GetJobParameter<string>("Connection");
        return new AutofacScope(_lifetimeScope.BeginLifetimeScope(config =>
        {
            config.Register(x => new SqlConnection(connection)).As<SqlConnection>();
        }));
    }

    class AutofacScope : JobActivatorScope
    {
        private readonly ILifetimeScope _lifetimeScope;

        public AutofacScope(ILifetimeScope lifetimeScope)
        {
            _lifetimeScope = lifetimeScope;
        }

        public override object Resolve(Type type)
        {
            return _lifetimeScope.Resolve(type);
        }

        public override void DisposeScope()
        {
            _lifetimeScope.Dispose();
        }
    }
}