I've been playing Spartan Ops on Legendary recently, and I've found the Knights to be far more problematic than any other enemy. Even Fuel Rod Cannon-wielding Elites are no big deal by comparison.

Knight Prep

Ideally, you want to get a few things in order before you engage:

• Weapons - I find that UNSC weaponry is less than effective against Knights. I will typically abandon an AR, especially, if I'm up against them. I will tend to try to get Covenant or Promethean weaponry if possible, although BRs and DMRs can make do in a pinch. Typically there are Promethean weapon racks near where you fight Knights, so be on the lookout. Sniper weapons are tough to use for me to use against Knights, since Knights tend to move fast and it's hard to keep an accurate shot lined up. This is a bit easier on Campaign than Spartan Ops - in Campaign their AI doesn't tend to jump around as much. Whatever your weapon of choice, make sure you've got a full magazine in both the weapons you're carrying.
• Groups - Split groups of Knights up if you can. Trying to fight more than one is not at all worth the effort. Their AI is smart enough to retreat when they're injured, and when you try to give chase their buddies will take you out. Knights will sometimes teleport to close range to try and surprise you, and this can be a good tactic for splitting one off from the herd - stay at a distance, and harass them a bit, and when one teleports close to you, run away from the others. Try to continue drawing the "sucker" away from the pack.
• Arena - Pick an area that's got fairly long lines of sight, since you have to keep the pressure on them, and they tend to teleport. Fighting in an area where they can teleport out of your line of sight for an extended period is going to make things take far too long, and you'll probably run out of ammo.

Knight Tiers

There are classes of Knights, although I don't know their names offhand. You can tell Knights apart by their "plumage" - the higher Knight tiers have more glowy orange crystal stuff jutting out of their shoulder areas.

The most dangerous by far are those who have an integrated binary rifle in their torso. Not only do they retain the close-combat damage of a Sword Elite, and a medium-range power weapon in their other hand, they've also got a long range sniper cannon. If you're solo'ing Legendary, these guys you cannot fight at a distance. If you see them charge their binary rifle, either run towards them so they stop using it and switch to some other gun, or dodge behind some cover. On Legendary, these guys hit with crazy accuracy, and it's usually a 1-hit kill. I tried jumping, juking, etc, and I would consistently die within 10 seconds of spawning if they fired this weapon.

Coming close second is the Incineration Cannon Knight. The Incineration Cannon is devastating in both short and medium range encounters, and on Legendary they have crazy aim. It does large amounts of splash damage, as well. There's no warning when they fire, so try to either rapid fire them with a sniper weapon, or close with a rocket launcher-type power weapon and off them quickly.

Against both of these top-tier Knights, use the most powerful weapon you have available. Don't be shy about obliterating them with a sniper rifle, binary rifle, incineration cannon, etc. These are the guys that will give you the most trouble in the least amount of time.

Knight Tactics

Note what weapons they've got and try to fight them at a distance where that weapon is at a disadvantage. For instance, many Knights have scattershot weapons, which makes them terrible at mid- and long- distance combat. Get a Carbine, BR, DMR, Light Rifle, etc for these guys.

If you can't consistently hit with your precision weapon (BR/DMR/Lightrifle/etc), plan to use both of your weapons before reloading - it's faster to switch to your off weapon than to reload your primary in most cases. Finding a good pair of weapons is therefore fairly critical. Especially on Legendary and against higher-tier Knights, plan to use your power weapon and then switch off to your precision mid-range weapon quickly, since it tends to take more than just one rocket/fuel rod/etc to down them.

The Knights have shields that you can take down, although they don't glow as brightly as the shields on Elites. Their shield is vulnerable to an overcharged plasma pistol shot (similar to Elites), so bear that in mind if you've got one.

Once the shields are down, it takes multiple shots to the head to bring a Knight down. They have "face armor" which you can sometimes see them drop. You have to pierce this first. If they retreat, their shields will recover, although if you've already blown off their "face armor" it will still be gone when you take their shields down on future encounters.

The other thing you can do is exploit their AI and the odd physics. For instance, when teleporting, typically a Knight is vulnerable. They can't move while rematerializing at their destination. This is a good time to lob a grenade, since you know they're going to be standing there for a second or so. Also, almost all of the enemies in the game have a slow, lazy jump animation that they can't break out of. If you get up on a little hill, they'll jump towards you, giving you sometimes 3-5 seconds worth of free shots.