https://developer.mozilla.org/en/JavaScript/Reference/Global_Objects/Date/parse
Например
// create 1 of June 2011 from Jun 2011
var period = new Date(Date.parse("1 "+period));
Вот то, что я думаю, вы хотите
<script>
var months = ["Jan","Feb","Mar","Apr","Jun","Jul","Aug","Sep","Oct","Nov","Dec"]
var result = {"d": [
{"PeriodID":8,"Period":"072011","BeginDate":1294268400000},
{"PeriodID":2,"Period":"052011","BeginDate":1293836400000}
]}
var aPeriod, period, periodMM, periodYYYY, periodText, beginDate, beginMM, beginDD;
for (var i=0,n=result.d.length;i<n;i++) {
aPeriod = result.d[i];
// period = new Date(aPeriod.Period.slice(2),aPeriod.Period.slice(0,2)-1,1,0,0,0);
// periodText = months[period.getMonth()]+" "+period.getFullYear();
periodMM = parseInt(aPeriod.Period.slice(0,2),10);
periodYYYY = aPeriod.Period.slice(2);
periodText = months[periodMM]+" "+periodYYYY;
beginDate = new Date(aPeriod.BeginDate);
beginDD = beginDate.getDate();
if (beginDD<10) beginDD="0"+beginDD;
beginMM = beginDate.getMonth()+1;
if (beginMM<10) beginMM="0"+beginMM;
periodText += " "+beginDD+"/"+beginMM+"/"+beginDate.getFullYear();
alert(periodText)
}
</script>