That's not what you need to fix your issue. What you need is just a flipper rebuild kit, and I'd do both left and right flippers at the same time. Your coils are fine, don't worry about those.
Here's the exact flipper rebuild kit you need: http://www.pinballlife.com/index.php?p=product&id=983&parent=172
This will rebuild both your left and right main flippers. This will make them feel new again. The only reason why you'd need a new coil is if they were heat stressed and warped to the point where you couldn't slip out the coil sleeves when you do the rebuild.
As for the player piano, you might have a switch that's getting a little flaky in there, but it's hard to say without knowing a few other things. Do you have your machine set steep enough? Is it leveled well?