2 corners flipped
Annoying cases? Not anymore!
(R U'2 R U'2) (R U R' U) (R2 U R' U) (R2 U R' U)
(U R U'2 R U'2) (R U R' U) (R2 U R' U) (R2 U R')
(U R' U') (R'2 U' R2 U' R' U R' U'2) (R' U R' U'2 R')
(R' U') (R'2 U' R2 U' R' U R' U'2) (R' U R' U'2 R' U)

Cases you probably didn't know you knew
z Sune/Antisune z'
z' Sune/Antisune z

3 corners flipped
Sune
(R U R' U R U2 R') U' (R U' R U R U R U' R' U' R2) U'
U' (R U R' U R U2 R') U' (R U' R U R U R U' R' U' R2)
(R2 U R' U) (R U'2 R U'2) (R U R' U) (R2 U R' U) - optimal
U (R2 U R' U) (R U'2 R U'2) (R U R' U) (R2 U R') - optimal

Antisune
(R2 U'2) (R' U R' U'2) (R' U R' U') (R'2 U' R2 U' R' U R) - optimal
(R' U' R U' R' U2 R) U' (R'2 U R U R' U' R' U' R' U R') U'
(U' R2 U') (R' U R' U'2) (R' U R' U'2) (R' U R' U' R2) - optimal
(R2 U') (R' U R' U'2) (R' U R' U'2) (R' U R' U' R2 U') - optimal

3+1 (for these cases I AUF such that the oriented corner is on ULB)
(R U' R' U) (R' F R F') (R U' R' U) (R' F R F') - optimal
(R' F R F') (R U' R' U) (R' F R F') (R U' R' U) - optimal
(U2 R' U' R' U' R U R U) (R2 U R' U' R U R') - optimal
(R U' R' U R U') (R'2 U' R' U') (R' U R U R U'2) - optimal
(U R U R' U'2) (R U R' U') (R2 U'2 R'2 U' R2 U' R'2) - optimal
(R U' R' U) (R U'2 R' U R U) (R'2 U' R2 U' R'2 U2 R)

4 corners flipped
Double Sune
(R U' R) (U R U R' U' R' U') (R'2 U' R U R' U' R U' R') - optimal
either (U R U' R) (U R U R' U' R' U') (R'2 U' R U R' U' R U' R' U')
or (R U R' U) (R U' R' U) (R2 U R U R U' R' U') (R' U R') - optimal
I use either alg depending on my mood 

Pi
(R U) (R2 U' R'2 U' R2 U'2) (R'2 U' R' U R U'2 R' U) - optimal
(U R' U'2) (R U R' U') (R2 U'2 R'2 U' R2 U' R'2 U R) - optimal
(U2 R' U'2) (R U R' U') (R2 U'2 R'2 U' R2 U' R'2 U R U')
either (R' U'2) (R U R' U') (R2 U'2 R'2 U' R2 U' R'2 U R U) - optimal
or (U R U) (R2 U' R'2 U' R2 U'2) (R'2 U' R' U R U'2 R') - optimal
I use either alg depending on my mood 

Fake Sune
(R U2 R' U'2) (R U R' U') (R U2 R' U'2) (R U R' U') - optimal

Fake Antisune
(R U') (R' U2 R U2) (R' U R U') (R' U2 R U2) R' U - optimal

Weirdo 1
(R U R' U') (R U2 R' U'2) (R U R' U') (R U2 R' U'2) - optimal
U2 (R U R' U') (R U2 R' U'2) (R U R' U') (R U2 R') - optimal
U2 (R U' R' U R U'2 R') U2 (R U' R' U R U'2 R') - optimal
(R U' R' U R U'2 R') U2 (R U' R' U R U'2 R') U2 - optimal

Weirdo 2
(R U2 R' U' R U R') U'2 (R U2 R' U' R U R') U'2 - optimal
U'2 (R U2 R' U' R U R') U'2 (R U2 R' U' R U R') - optimal
(R' U R U') (R' U2 R U'2) (R' U R U') (R' U2 R U'2)* - optimal
U2 (R' U R U') (R' U2 R U'2) (R' U R U') (R' U2 R)* - optimal
* Note that these algs twist the DBR corner instead of the DFR corner like all the other algs do

When I say optimal, I mean 2-gen optimal, I don't know if these algs are 6-gen optimal, but I'm guessing most of them are.

Parentheses are not meant to indicate regrips, they're meant for easier learning of algs by "fingertrick groups". Most of these algs require at most one regrip. And there are lots of Air Jeffs and U'2s. I can't do left index-middle double triggers, but left index double flicks work fast enough for me. I also do right thumb followed by left index for some of the U'2s.

I can sub-2.5 on average for every single one of these algs, some are even sub-2, so they're not slow 

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Edit:
This is how CO works for me...
If more than 1 corner misoriented on U
1. Look at U, identify case. Place finger on affected D corner, if any.
2. z2 rotation, look at D, identify COLL case.
3. Don blindfold, orient D.
4. z2, orient U, done.

Why this way? I'm much more familiar with my COLL algs, so once I identify them, I execute them instantly. While executing them, I have time to think about the U layer alg which I may not be as familiar with.

I learned "all 4 directions" for most cases because AUF is something we unknowingly waste a lot of time trying to visualize, memorize, recall, and execute. How many times have you done some alg that starts or ends with some kind of U turn, and end up doing U3 instead of U', or U-pause-U, instead of U2, because you were *thinking* of the AUF? BLD is for braindeads.

Also, all those annoying cases with 2 corners misoriented on U (which are not COLL cases) are essential. This guarantees a one-look-at-U, one-look-at-D, no-funny-cube-rotations, minimal-AUFs CO system. With this system, the entire memorization + execution process of CO should easily be sub-10 with less than a week of practice. I found most of these algs yesterday and I'm averaging 11.xx now.

Oh, and...
If 1 corner misoriented on U
1. z2 rotation to D, identify case, take note of AUF and ADF.
2. Don blindfold, orient, z2, done.