So What Exactly you need?
A whole code?
What you have tried?
Follow this:-
Bind dropdown simply with a datatable that will have dates and other one with time
On selected Index Changed event write your logics.
This way you can handle dates:-
var dtDate=new DataTable();
dtDate.Columns.Add("AppointmentDate",typeof(string));
for (var day = 0; day < 59; day++)
{
var drRow = dtDate.NewRow();
drRow["AppointmentDate"] = DateTime.Now.AddDays(day).ToString("MM/dd/yyyy");
dtDate.Rows.Add(drRow);
}