You can query between two dates by using standard SQL syntax, but you need to assign the dates as date parameters to the OleDbDataAdapter. Otherwise it will treat the dates as text and you will not get proper matches.
DataSet ds = new DataSet();
using (OleDbDataAdapter dataAdapter = new OleDbDataAdapter(SQL, conn))
{
// Format the dates as dd/mm/yyyy
string date1 = DateTime.Now.AddDays(7).ToString("dd/MM/yyyy");
string date2 = DateTime.Now.ToString("dd/MM/yyyy");
// Set up the SQL with the two date paramters
string SQL = "SELECT [Req Start Date] FROM [CR$] WHERE [Req Start Date] BETWEEN ? AND ?";
// Assign the two dates
dataAdapter.SelectCommand.Parameters.Add("@p1", OleDbType.Date).Value = date1;
dataAdapter.SelectCommand.Parameters.Add("@p2", OleDbType.Date).Value = date2;
// Run the query
dataAdapter.Fill(ds);
}