Delagina:
Manual digging would certainly be possible, with enough men, shovels and 5-gal. buckets to haul the soil away. You said drilled shallow piers, so in either case, the soil has to stand on its own during the process, unless you case the hole, and/or form the footing. You haven’t really defined the whole problem/project or the loads, sizes, etc., so there is much still to be brought into the planning. You also have to be able to get rebar and enough concrete in there in a timely fashion to complete the piers or footings without a hundred cold joints. What I suggested is fairly common equipment, nothing real special, so any contractor who you want working on the job will be able to get his hands on the right equipment, and include it in his costing.