You can use the following code for DayPilot Month:
function invokeMenu(start) {
var selection = new DayPilot.Selection(start, start.addDays(1), null, dpm);
menuCreate.show(selection);
}
TimeRangeSelected event must be handled on the client side:
TimeRangeSelectedHandling="JavaScript"
TimeRangeSelectedJavaScript="invokeMenu(start)"