Ah, right down my alley.

Make sure you have the Thief mundus stone on, along with medium divines armor and sharpened weapons.

Put all points into stamina; it raises your weapon damage and you get more stamina for more sustained damage output. Don't worry about survivability; usually it's on the healer to do that anyway.

If you're still struggling with health issues, feel free to replace your Hunding's Rage armor with Twice Born Star and grab the Shadow mundus stone as well. I've done some testing and even when solo on a target skeleton, TBS still does more damage, but Hunding's Rage and Night Mother's Gaze come in at a very close second. (EDIT: More testing shows that NMG does more damage than TBS, but the results are pretty all over the place with the 3mil target skeleton. Lets just say that their differences are negligible.)

For the monster set, you might want at least 1pc Kra'gh's. It gives physical penetration just from the 1pc and it's still the BiS monster set for stam users as far as I can tell. The second piece, you can go with another piece of Kra'gh's, Velidreth, or Molag Kena. Again, medium divines.

Put max stamina enchantments on all your armor pieces.

Your jewellery is a bit all over the place, to be honest. The BiS choice for jewellery would be 3pc VO (Vicious Serpent) jewellery; they drop from Craglorn trials. However, those are quite hard to farm; the second choice would be to go for 3pc Agility, since they grant a nice boost to weapon damage. Make sure they're robust, and put weapon damage enchantments on them. If you find yourself struggling with health, you can go with healthy Agility pieces as well; those traits actually give you quite a nice boost to your health pool at 924 health per piece.

As for your weapons, you can use any 1h weapon type you want, though I would recommend either dual daggers or a dagger-axe combo. Sharpened, one with the crusher enchantment, the other with weapon damage. Your bow should also be sharpened with a weapon damage enchantment as well.

If you can do vMA, get to farming for that Maelstrom bow, at least; it's so good and will make your Endless Hail your main and best DoT. For dual wield, get the Maelstrom dagger and Maelstrom axe. Again, all sharpened.

For CP, you can do anything with your points in the red tree, though people would recommend splitting it between Hardy and Elemental Defender. In the green tree, put all points into stamina cost reduction, and the rest into stamina recovery. In the blue tree, all into Mighty, and split the rest between Thaumaturge and Precise Strikes; split that any way you want, though you should want at least 50 in Thaumaturge.

Onto skills, the part which matters the most.
I'll just post what I have.

Frontbar:
Venomous Claw, Rending Slashes, Rearming Trap, Bloodthirst, Camo Hunter, Flawless Dawnbreaker.
Backbar:
Igneous Weapons, Poison Injection, Endless Hail, Noxious Breath, Flames of Oblivion, Standard of Might.

Skills for flexibility: Razer Caltrops, Unrelenting Grip, Green Dragon Blood, Dragon Fire Scale, Igneous Shield, Steel Tornado, Acid Spray.

That is my target skeleton parsing skill line up. I can parse 36.5k solo on target skeletons on my Argonian stam DK (1pc Kra'gh's, 1pc Veli, 5pc TBS, 3pc VO/Agility, and Maelstrom nirn dagger, sharp axe, sharp bow, all golded out, with weapon damage/crit/stam potions).

In a dungeon where the healer is less-than-elite, I swap out Flames of Oblivion with Resolving Vigor. I also sometimes replace Noxious Breath with Razor Caltrops. Igneous Weapons is also another flex spot; if you have a DK tank in your group putting that buff up along with the Mountain's Blessing passive regularly, you can swap that out with more survivability or more damage skills. In trash pulls, you can just swap out Rending Slashes with Steel Tornado.

Also, I'm using Bloodthirst instead of Rapid Strikes. Rapid Strikes may be more dps, but Bloodthirst's sustain is insanely useful, and is pretty much a must-have if you're even considering vMA. Stick with Rapid Strikes for now if you're going to stick with dungeons. I'll just call both Flurry from now on just to avoid confusion.

In any typical DPS rotation, lay down all the DoTs you have available and use your spammable while you no longer have DoTs to cast while they're ticking. Always refresh DoTs at the end of their cycle. Your spammable would be your Flurry.

One thing good about a stam DK is that their DoTs always tick for ~10 seconds, so that makes for a very stable rotation.

One more thing; only ever use your Standard of Might ulti, unless the boss does not have enough health for you to gain ulti for another Standard of Might, in which case, just burn your Flawless Dawnbreaker.

Non-vMA-weps rotation: Poison Injection, Noxious Breath, Endless Hail, Venomous Claw, Rending Slashes, Rearming Trap, Flurry x3-5 (depending on when your first DoTs finish), then back to the beginning. Start off with Igenous Weapons and Flames of Oblivion. Drop Standard right after your first rotation. Refresh Igneous and Flames every second rotation, alternating; you can ignore Igneous if your tank is giving you the Mountain's Blessing passive and you are running weapon power potions. Since you're at high ping, I don't recommend that you weave in light attacks too much; maybe just between your Flurry spams.

vMA-weps rotation: Endless Hail, Noxious Breath, Flames of Oblivion, Flurry, Venomous Claw, Flurry, Rending Slashes, Flurry, Rearming Trap, Poison Injection, then back to the beginning. Start off with Igenous Weapons and Flames of Oblivion. Drop Standard right after your first rotation. Alternate between Igneous Weapons and Flames of Oblivion with each rotation; again, you can ignore Igneous if your tank is giving you the Mountain's Blessing passive and you are running weapon power potions.

This is, by all means, the meta stam DK cookie cutter build. I highly suggest you analyze this build and discover what makes this build tick, and I encourage that you do some testing on your own and change things around to fit your playstyle.