I am building an outdoor storage shed 9ft X 12ft. I plan to use concrete peirs that are 8"-10" in diameter for the sheds foundation.
I have been able to dig holes for the 9 peirs but can only go about 2 feet deep easily. I would like to go deeper but it would take a lot of additional effort. What is the recommended diameter and depth for this size and type of building?

Depends on where you live... the depth will vary because you want that below the frost line as soil above that heaves when it frezes and thus isn't stable. If its because you are in eastern Texas and are on the bedrock that is so close the surface.. then you would be good... I assume that's the problem you have at 2 feet depth.

8-10" piers seem a bit overkill for a 9X12. If you are not in a tornado area and in a temperate climate, GA, FL, etc. just lay 3 PT 4X4/12 on the ground, build your floor frame and use mobile home tiedowns to anchor the 4X4. HD and Lowe's do it all the time in the Atlanta Area. My building is 10X12, in the GA Mtns and has survived for 10 years built like this. However, depending on where you live you may have a code or heave issue.

Check the building code for your area. Some codes call for piers and will specify what you need. Other codes like mine and ma0641 call for very little. I have a 10x10 shed that sits on PT 4x4 for nicely for 20 years even through our tornado like past summer.

Is that the tornado you sent to Atlanta last year?

Yea, and we are brewing another one tonight and again tomorrow. Chicago is windy but that's not how it got its name.