Technically speaking, without counting symmetries, there are only two cases for a permutation of corners in a layer: adjacent swap (AKA T permutation) and diagonal swap (AKA Y permutation).
What you probably want are algorithms that permute and at the same time orient the corners of the second layer, while first layer is being solved. Search CLL.
If you want to permute and at the same time orient the corners of the second layer, while a face of the second layer is being solved, see EG method. Section called External links provides the algorithms.
You can always generate your own algorithms if you don't like those linked ones for some reason.