Ignition coil broken inside tube

I use something like a long sheet rock screw or if there is room next to it a curved tip pick. With the screw you can tape it to a screwdriver get it to bite into the core in the middle of the coil and then use pliers or a wire wrapped around it to pull the piece out.

When you say it broke off, I assume you mean the boot part of the coil? If so, you will need use long narrow needle nose pliers to reach down there and pull it out. If not, you will most likely need to remove the rocker cover. Once you remove the rocker cover you should have more room to pull it out.

Take a look at this diagram to see what I am referring too.

Let me know if this doesn't make sense or what questions you have.