Generally pistons on modern cars are only meant to come out upwards along with the con rod minus the big end cap and often only one side of the crankshaft usually with crank at bottom dead centre for max. clearance.
If you are saying it has gone down so far when working on the big end cap that the piston rings have sprung out , then the only thing I can suggest is using a couple of flat screwdrivers to ease the rings back in as you push the piston back up the bore.
I am trying not to make any rude comments, but it does sound like a little more care required.
Any persuasion I would do with a gentle knock using a piece of wood so as not to damage anything.