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.

My buddy did NF (cables) on Thursday. The snow is consolidated and most of the eye bolts are exposed. You will need an axe, as there's plenty of snow/ice.

Flying Dutchman and Notch Couloir both looked really good. We did Dreamweaver and there was some loose rock and delaminated ice, but nothing too heinous.