FFS staples are the worst!
I've had a machine that rails came up nice and easy with a rigid putty knife, but one that wouldn't even budge.

Hopefully with a little upward pressure and moving to diff'rent areas around the staples they'll come up. Then you can drill new holes for screws when you put them back on.

I'm not quite sure what you mean--the terminology you're using isn't quite right. Are you talking about the wooden playfield rails on the edges of the playfield? The plastic channels on the top edges of the cabinet that hold the glass? The long metal siderails on the cabinet?

For removing staples, look for furniture staple remover/puller tool. I've used Berry's removers, although the more modern puller looks interesting.

If you're removing metal siderails, putty knife to separate the siderail from the cab slightly, then use vampliers to pull the nails out. Depending on how proud the nail heads are, you might be able to skip the putty knife and just pull the nail heads.

Plastic pry tools for automotive interior trim work very well for removing the wood rails.

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Usually if you rock them sideways back and forth they will loosen enough to get a mini flat pry bar under them.

I just removed my Eight Ball rails this way. After removing the screws, bend back and forth until you get some space between the rail and playfield and then use something to pry it. This was easier then expected.

My staple puller wasn't strong enough to pull the rail staples. It would just bend the tip of the puller. If you aren't too concerned about damage on the playfield you are getting ready to throw out, get something a bit more stout (like a old flat screwdriver sharpened a bit) and drive it under the staple head to raise it a bit and then use a old fashioned prybar. Another option is to cut the staple's head in the middle, pry up the two sides and clamp a vise grip on them one at a time (making a clamped on nail head) then use a prybar to pull them out. Once you get a couple out on one end, a stiff spackling knife inserted on the loose end can "wiggle" down the rail lifting it from the playfield. Wedge it off, don't pull it off, it might split and you need it.

Super easy way to remove the staples, just finished doing this to my centaur a few minutes ago.

Give the ends few taps with a hammer until there is enough room on the other side to get a set of needle nose pliers on them.

Grip the loop with the pliers, then hit the pliers with the hammer until they come out.

This way you’re not marring up your old playfield in case you’re going to reuse it for something and those staples aren’t on the floor or flying across the room for someone to find later with their foot.

This is a great method. Just one small addition…
When tapping the ends of the staples, lightly hold them in needle nose pliers so they don’t bend as you hammer them.