If you just want to show users the year and month dropdowns, you can add the following to your date field. It hides the Day dropdown and sets the value to 1 (first of the month):
$(document).ready(function() {
// Identify this question
var qID = {QID};
var thisQuestion = $('#question'+qID);
// Hide the day dropdown
$('select.day', thisQuestion).hide();
// Set the day to 1
$('select.day option:eq(1)', thisQuestion).attr('selected', 'selected');
// Hide the first separator "-" character
$('.answer-item', thisQuestion).contents().not('label, select, input, :empty').wrap('');
$('span.date-separator:eq(1)', thisQuestion).hide();
});
