You can use the editable select jquery plugin from here. Make sure to use the included CSS and JS files.

Here's a sample form with a table that has a drop down field. The drop down field uses the CSS class name, tabledropdown. After applying the following JavaScript

$(document).ready(function () {
  $.getScript('http://myserver/Forms/js/jquery.editable-select.js', function() {
    $('.tabledropdown select').editableSelect();
    $('.cf-table-block').on('click', '.cf-table-add-row', function () {
      $('.tabledropdown select').editableSelect();
    });
  });
});

the form now looks like

where the user choose from an existing option or input their own. You'll have to replace "myserver" with your actual Forms server.