The broken coil frame is just putting a little strain on the coil wire. A little hot glue might be all you need to make it right. It has nothing to do with the coil buzzing. That might be a worn out coil stop, which helps to suppress buzzing when it's working.

Replace the coil if you don't like the broken frame, but it probably won't fix the buzzing.

/Mark

Look at the end of the plunger. Thes get cupped and don't seat firmly to the stop causing the buzz. I like to file the end of the plunger flat and sometimes replace the stop.

Buzzing AC flippers are quite common. I have put in a complete rebuild kit, only to have it buzz, so just firing all new parts at it will not fix it.

Some things to try:
- Make sure none of your parts have excessive wear. If it is due for a rebuild kit, put it in first.
- Make sure everything is tight and in alignment.
- If it still buzzes, take it apart and put it back together (seriously). Mess with the alignment of the parts slightly.
- Maybe stick a wave washer in there like some of the Gottliebs use.
- If you are fully glitched out, and really can't stand it, put in a rectifier and run off DC. The flippers will be considerably more powerful and this change will likely result in broken playfield plastic, but you can ease your tortured soul knowing your flippers are quiet.

Edit: My bad, this is not a flipper coil. Is it a gate coil?

Anyway, my advice above still holds, other than the rectifier would be a much more viable solution. You could add a couple of diodes and make it half wave rectified.

Once you realize it’s just micro tolerances causing the buzzing. You will be a whiz at fixing this problem when nothing seems to work. My personal view is replacing is not the real solution. You are changing the tolerances and getting lucky. Do the easy stuff first sleeve etc. Then do the hard stuff. This can include bending links that steel bushing go in or making roll pin bigger by hammering or using vise to make them a little tighter. If you can move it side to side by hand and it seems sloppy. What do you think a badass coil is going to do when powered up? Just don’t over do any of these! We tend to gorilla stuff. Take your time and don’t be the gorilla!

Oh and take your shit off the playfield before beating on it!