How can I swap opposite corners on the same face of a 2x2 Rubik's cube?

Question

I've been experimenting with using Y-permutations to solve the 2x2 cube as described here. I ended up with the cube solved but for a single face where the opposite corners were swapped and disoriented. I managed to solve the cube, but I wonder if there is a shorter algorithm to accomplish this task.

Answer 1

If you rotate the face one quarter-turn, you will have a 3-cycle to solve. That may be easier.

ADDED IN EDIT

Ouch! not a 3-cycle but a product of two 2-cycles, but still an even permutation.