I do not think that the square stones look good or right at all. I would keep the original coping to be honest. Why do you want to change it? If you do really want to change it, I would remove the coping that is there and add new coping of the same style.

What you show in the photo (new stacked on original) doesn't look good.

What are you trying to achieve with the backyard update?

It's a 1974 poured concrete pool. White coping is failing - cracked, crumbling - and all the pavers around also were failing and will be replaced.

Thank you - both your comments align with mine - the proposed "new stone placed on original/white coping" doesn't look good, not to mention it raises the height - impact to stairs, etc.

Have calls in to companies who specialize in repairing the coping on this type of old pool...

And if the old coping is failing, why would you stack new stuff over it? Sounds like they want to mask the failing coping with some "mortar" and top off with new coping. Just enough time will pass, before it all starts to fail again that they will claim they aren't responsible!

Definitely get a company that specialized in actual pool repairs.