There is usually a early snow in the first week of Sept, then glorious weather, but there is no predicting when the first storm will hit - - and for three or four days it is darn cold and wet. June is similarly unpredictable, but with the advantage of a wildflower bonanza late in the month.
The peak tourism months are July & Aug (ca 900,000) - followed by June & Sept (ca 600,000).
Of the 3.5 million visitors in 2011 - 3 million came during June thru Sept.
My choice would be the last two weeks of June or the last two weeks of August.
PS - you may need a permit for your group.