Are the plungers missing? Reason I ask is because I've seen melted coil before but never anything so bad that I couldn't reuse the plunger after some clean up.
As to why they melted. - It's almost always a stuck switch causing the coil to stay energized way longer than it should, Could simply be a stuck playfield switch or could be a switch on a relay not opening properly. Best thing to do would to look at the schematic and see what switches trigger these particular coils and make sure they are all opening and closing as they should, and are not sticking in one position.
By the way - The 2 worst melted coils I've ever seen were in games where a previous owner bypassed a fuse. One had an alligator clip jumper wire which also melted and the other had a #12 solid Romex looped over it. I have no idea how that one didn't burn up completely. So I would check to make sure no one did any funny stuff to the fuse block, just in case.