Either some one who directly benefits from extended war IE. Cyrus or some one who can afford extended war IE. Darius, they both have the same civ which also includes the Immortal which is the 3rd or 4th best UU for this purpose.
Cant go wrong with either.
I disagree completely. There is NO WAY you can win a domination victory using Immortals. They are worth a damn only in the very early game, and might be used for an early rush, but that contributes nothing whatever to a domination win, except giving you a good start on the game. You don't end up with more population or territory after an early rush than you do after the same period of expanding with settlers. Like all victory conditions, domination is a long-term thing -- well, it is unless you're playing on a Tiny Pangaea map with only two or three civs.
The way to win a domination victory is to expand in stages, conquering one opponent at a time, then peacefully consolidating the gains. There are basically four windows of opportunity, not counting an early rush (which some players seem to focus on as if it were the be-all end-all).
The first is when you have the following techs: Iron Working, Construction, Code of Laws, and Currency. You need the first two for your military force, and the second two for your economy to be able to support a good-sized army and be able to assimilate your gains. (Remember, in domination, unlike conquest, you don't want to raze cities, you want to keep them.) You'll build a mixed force of Swordsmen, Spearmen, and Catapults, and if you have ivory you'll add War Elephants to the mix. You'll go on researching during the war, and when possible upgrade your Swords to Maces. (Unless you're playing the Romans -- the Romans have a HUGE advantage during this phase, but this phase alone won't win a domination victory.) You'll stop and make peace when you start running into Longbowmen and Crossbowmen, which are better defensive units than your Maces can handle without unacceptable losses, or when you've wiped an opponent or two and taken all their cities and you think the next one would present that problem.
The second window comes with Guilds and Engineering. You'll field a force of Knights, with Longbows, Crossbows, and Pikes for defense and occupation, and Catapults or Trebuchets for city defenses. The Knights are your attack units. Again, you'll upgrade during this war to Cuirrasiers/Cavalry, Riflemen, and Cannon. This window closes when you start running into Infantry, which again puts too much strength in the defense.
The third window comes with Industrialization, Artillery, Flight, and Radio. Your new force will consist of Tanks, Marines, Anti-Tanks, Artillery, Bombers, and Fighters. By building Jails in all your cities, plus Mount Rushmore and adopting Police State, you can reduce War Weariness to zero, and all of those should be available at this time. No upgrades here, because Mechanized Infantry, which eat Tanks for breakfast, are available before Modern Armor which are the only units that can answer them. So when you start running into Mech Inf, time to make peace for a while.
The fourth and last window is with the most advanced units: Modern Armor, Mechanized Infantry, Mobile Artillery, Jet Fighters, Gunships, and Stealth Bombers. No more stops after this, just go for it.
A domination victory is normally won during that third or fourth window. Once in a while it can be won in the second. If you win it in the first, you need to up the difficulty level or play on a bigger map or a non-Pangaea. (Pangaea is just too easy for any sort of military victory. If you want a decent challenge, play on something that requires going to sea.) And if you win it with an early rush using Immortals, you need to play on harder difficulty, on a non-Pangaea, and with more than one opponent.
The difference between Domination and Conquest is that in a Conquest victory you are trying to destroy all other civilizations, not gain and hold land and population. So after you've grown big enough to support extended military action with a huge army, you don't keep any more cities. Just burn them all down. Obviously, though, for Domination that's counterproductive.