I haven't been up there, but your post caught my attention because I'd like to give the Kiener's a try this year. Anyways, I went onto the National Park website and found a fairly recent update on conditions. Hope it helps!
Trail: Longs Peak
Date: 6/3/12
By: Visitor
To Peacock clear. 2 snowfields to Chasm. Chasm Lake ice 1' thick but starting to break up. Several feet hard snow around lake (walkable). Lambslide: posthole 1' whole way. Alexander Chimney & Couloir-90% snow filled. Diamond-considerable water due to melt. Loft to Clark's Arrow- downward totally free of snow. Keplingers- nearly free of snow, passable with hiking boots. Keplingers to Homestretch is snow filled to Notch. East Face: lots of snow in the Couloir Route, down into the Notch. Upper pitch of Notch Couloir- all wet downward. Homestretch- snowy ledges. All the way to Keyhole little snowy & icy. Trough- still full of snow, but passable. Keeners-lots of snow. The Drunken Frenchman and North Face- lots of good snow coverage that will be good travel if there is a hard freeze.