For resolving different objects, are there any alternative coefficients to the one used in the Rayleigh criterion? (which is 1.22) http://en.wikipedia.org/wiki/Angular_resolution#Explanation
It's the point where you can't distinguish between the maxima and the first minima.
But could there be cases where you have a more stringent limit? Or a more generous one?
 A: Oh yes, sure.
Imagine you're looking at a close double star. When do you declare it "resolved"? The most strict definition would be when there's a vanishing sliver of dark in between the two Airy disks of the star components of the doublet. That corresponds to the criterion you mentioned above - actually, twice that, since the first diffraction minimum of one star is riding on top of the first minimum of the other star.
But really, do you need that much separation to tell this is not a single object? No. Let's say, when the Airy disk is oval, and the oval starts to exhibit a narrow band in the middle (starts to look like an hourglass), that's when you can pretty much tell that's actually 2 Airy disks overlapped.
However, if all the other Airy disks in the eyepiece are round, while only one of them is oval, it doesn't even need to look like an hourglass to suggest there's something going on with that "star".
It really depends on what the final goal is.
A: 1.22 also comes from the position of the first zero of the Bessel function.  The Bessel function is what describes the image plane illumination from a circular aperture, the most common type.  A square aperture will give you a different difraction pattern and hence the factor of 1.22 can be different.
Having re-read your question I would also remark that there are some fancy aperture shapes that have 'Inner' and 'Outer' working angles, where different parts of the image plane achieve levels of contrast quite different to an Airy disc.
A search for 'Spergel' masks should show some of these different designs.
