Several ways to do it and I'm sure others will post with their preferred methods, but I like to use a grease gun. I just unstuck a 550 caliper piston that sat unused for the past 20 years. Air, up to 120 lbs. wouldn't do it. The hand grease gun got it out in 30 seconds.
Just remove the bleed fitting, install the threaded hose connection from the gun and pump away. It's important to note that the threads won't be the same, so be careful here. Thread the hose in lightly until you feel resistance. You just want to get it to stay in place.
It should go without saying, but be sure to clean the caliper afterword. No grease can remain in there.