We live in New England where we have very large rocks all over our property. We are building a 16 X 22 shed and would like to use our rocks for our corner posts. Would it be structurally sound to dig a hole similar to a sono tube size but layer our rocks with concrete?
If it take more than one to fill the hole, you don't have "very large rocks" for New England.
Plenty of old barns and other buildings are sitting on large rocks (4 feet or more in at least one direction) that were rolled into holes to provide a solid, dry, non-rotting foundation hundreds of years ago, for hundreds of years.
You appear to be talking about something more on the lines of a mortared pier built of comparatively small rocks - one issue with those is that they are more prone to frost movement (.vs. a sonotube or formed concrete pier of another shape, such as a tapered square pier) because the outer surface is rough and frozen soil is more prone to "grab and carry" it rather than slip past it in freeze/thaw cycles.
You might want to look at "slip forming" where you'd set a form and then build with your rocks and concrete resulting in a smooth outer surface, at least for the below-ground part. Almost any New England library is likely to have a copy of Helen and Scott Nearing's "Living the Good Life" which happens to include a chapter or two on slip-forming (and at least one "really very large" New England rock, as I recall.) That was more oriented towards full foundations, in their case. Another approach is to use sonotubes below-ground and mortared rocks above ground.
Depending on the purpose and nature of the shed, another option is to not worry about frost movement at all, and just set your piers on the surface of the ground and let the building float - again, many examples of old buildings built this way exist, though of course we only see the ones that survived this long, now.
There are two major issues with “large (or small) rock foundations”: 1) set all the footings down at the same level, and 2) set the bottom of the foundation below the frost line.
Assuming the soil has about the same bearing capacity throughout the building area at each depth below the building. You want all your footings at the same depth so that you do not have differential settlement.
The bottom of the footing must be below the frost line or it will heave and cause movement in the foundation. Then the rocks will crack and allow water into the foundation allowing more cracks.
Make all the footings the same, install them all at the same level, and start below the frost line.