The first thing that came to mind was the Bahraha's Curse set.

vesselwiththepestle's question is important, though. Non-DLC normal dungeons are no challenge at all, e.g. you can solo them as a DD, except where mechanics forbid it (Blackheart Haven etc.). Even on veteran mode about half of them can still be soloed. Get on to DLC vet dungeons, though, and you probably need a 4-man group, unless you're going for a world-first, let's use every trick in the book kind of run.

I agree, if you are duoing stuff, go with a tank and DD, but go with 2x DD for the easier stuff. I PvP and I always think a well-rounded solo PvP and/or vMA build is also suited to soloing dungeons. I'd still call those fundamentally DD builds. I find either a magplar or stamsorc the easiest for soloing / duoing. They both provide strong healing while attacking. My PvP magplar build:

https://en.uesp.net/wiki/Special:EsoBuildData?id=95564

Note this IS my PvP build. For PvE, I make the following changes:

Blazing Spear instead of Degeneration
Elemental Blockade instead of Total Dark
Skoria instead of Pirate Skeleton for the easier content or in 4-man groups

What's noteworthy about this build is the build pattern, namely:

3x Protective jewelry
Defensive monster set, as needed
1x damage / regen set (Amber Plasm)
1x damage set (Overwhelming Surge) on front bar
vMA resto back bar, if you have it, or any resto otherwise
Light armor. Templar damage really plummets without it.

Instead of Overwhelming Surge, any damage set will do, such as Julianos, Mother's Sorrow, Spell Strategist, and so on. Instead of Amber Plasm, any damage + sustain set will do, such as Bright Throat's Boast or Shacklebreaker. If you can't make Protective jewelry, then consider Fortified Brass.

I am, unfortunately, no expert at building tanks. In terms of class, I believe DKs are still the go to, with a Nord DK probably optimal. A 1-hand + shield / blocking playstyle is the standard. Build for high health, around 35K to 40K, as well as high resistances. Heavy armor. Sets for solo / duo include:

Bahraha's Curse (AOE damage reduction, damage and self-healing)
Cyrodiil's Crest (powerful self-heal while blocking)
Battalion Defender (same idea)
Fortified Brass (get your resistances up)
Blood Spawn (probably still the gold standard, esp. for DKs)
That new monster set that gives you resources after blocking

You only really need a tank for the DLC dungeons. The tank has to taunt the monsters and bosses that might otherwise one shot you. No amount of healing helps a healer or DD, when they are at risk of being one shot. Tank + DD is the way to go for DLC dungeons alright. A tank + healer group could also work, but would be slow and frustrating. I'd err on the side of making a self-healing DD, rather than making a healer with some damage, although with a magplar the lines can get very blurred. Magplar + DK tank is probably your best bet, if you intend to duo DLC dungeons, with the magplar throwing the DK shards for stam sustain.