Sean answer is pretty good, if you want to disable day selecting as well, you might use a different approach, you can see the result in this fiddle:

Calendar is hidden, so you can only choose month and year. When selecting a date in first datepicker, minDate of second datepicker is getting adapted.

EDIT

jQuery datepicker has seriously problems when dateformat doesn't provide a day. I changed th code to make it work. Only thing is when opening a datepicker, I have to convert the date to a suitable format. Have a look at the new fiddle.

HTML:

<p>Date: <input type=text id=first-datepicker/></p>

<p>Date: <input type=text id=second-datepicker/></p>

CSS:

#ui-datepicker-div .ui-datepicker-calendar,

#ui-datepicker-div .ui-datepicker-current

{

    display: none !important;

}

JAVASCRIPT:

$('#first-datepicker').datepicker({

    changeYear: true,

    changeMonth: true,

    beforeShow: function (input, inst) {

        setMyDate(inst);

    },

    onClose: function (dateText, inst) {

        saveMyDate(inst);



        var secondDatePicker = $('#second-datepicker').data('datepicker');

        var dateSetted = secondDatePicker.input.data('date-setted');



        setMyDate(secondDatePicker);



        secondDatePicker.input.datepicker('option', 'minDate', new Date(inst.selectedYear, inst.selectedMonth, 0));     



        if (dateSetted == true) {

            saveMyDate(secondDatePicker);

        };

    }

});



$('#second-datepicker').datepicker({

    changeYear: true,

    changeMonth: true,

    beforeShow: function (input, inst) {

        setMyDate(inst);

    },

    onClose: function (dateText, inst) {

        saveMyDate(inst);

    }

});



function saveMyDate(inst) {

    inst.selectedDay = 1;

    inst.input.data('year', inst.selectedYear);

    inst.input.data('month', inst.selectedMonth);

    inst.input.data('day', inst.selectedDay );



    var date = new Date(inst.selectedYear, inst.selectedMonth, inst.selectedDay);

    inst.input.datepicker('setDate', date );

    formatDate(inst, date);

    inst.input.data('date-setted', true);

};



function setMyDate(inst) {

    var dateSetted = inst.input.data('date-setted');



    if (dateSetted == true) {

        var year = inst.input.data('year');

        var month = inst.input.data('month');

        var day = inst.input.data('day');



        var date = new Date(year, month, day);

        inst.input.datepicker('setDate', date );

    };

};



function formatDate(inst, date) {

    var formattedDate = $.datepicker.formatDate('MM - yy', date);

inst.input.val(formattedDate);

};