This is not done out of the box for the CssOnly mode.
You can add your own class to the background cell using BeforeCellRender event handler:
protected void DayPilotScheduler1_BeforeCellRender(object sender, DayPilot.Web.Ui.Events.BeforeCellRenderEventArgs e)
{
if (e.Start.DayOfWeek == DayOfWeek.Saturday || e.Start.DayOfWeek == DayOfWeek.Sunday)
{
e.CssClass = "scheduler_green_cellweekend";
}
}