The best way to deal w/this is a complete disassembly and cleaning, and using an overhaul kit. You probably have enough of a buildup of corrosion that things are not going to move easily, if at all.
If you decide to follow Mike's instructions but you can't get one piston to move with using compressed air to force the stuck puck out, I have the solution. Notice your bleeder valve (some calipers have 2)? What is it shaped like besides a bleeder valve? Ever greased a suspension fitting? There is your answer. Use a grease gun to pump the caliper full of grease. I guarantee it will come unstuck where it won't if you try the compressed air method and nothing budges!
I did this helping a friend re-do his CBR600 F2 front brakes. We went to a garage to use their compressor as he didn't have one, and when that didn't work, I suggested the grrease gun, and it immediately moved the piston where repeated attempts w/air pressure failed to budge it. Try it- it works every time!
If you already removed 1 piston, you will have to reinstall it and replace the pads so you hold that one already loose in-place while you allow the other one to move. A c-clamp can hold one piston stationary while you force the other one w/the grease.