He usadohttps://datatables.net/reference/api/rows.add%28%29 enlace funcionando pero los datos que muestran la tabla como[object,object]. Cómo mostrar el objeto a la cadena. He usadoJSON.stringify(obj) Tampoco funciona.

HTML

<table id="exampleTable">
 <thead>
  <tr>
   <th>Year</th>
   <th>Month</th>
   <th>Savings</th>
  </tr>
 </thead>
 <tbody>
   <tr>
    <td>2012</td>
    <td>January</td>
    <td>$100</td>
   </tr>
   <tr>
    <td>2012</td>
    <td>February</td>
    <td>$80</td>
   </tr>
 </table>

JS

$('#addRows').click(); 

var table3 = $('#exampleTable').DataTable(); 

$('#addRows').on( 'click', function () { 
    table3.row.add(
       [ { "Year": "Tiger Nixon", "Month": "System Architect", "Savings": "$3,120" },
         {"Year": "Tiger Nixon", "Month": "System Architect", "Savings": "$3,120" }]
    ).draw(); 
});