Maybe something like these. I have a pair for working in the yard, and they're grippy.
They have other styles that have grippy nubbins on them too.
There's also rubbery/non-slip drawer liner material.
ETA: Not Stihl brand, that sounded kind of confusing.
Drawer liners WalMart/Lowe's/Dollar General, stores like that.
I've cut those into smaller pieces to use for various things, they're great for opening jars, and I bet that would work for the Kayfuns too.
I moved recently and I have some of that rubbery drawer liner. I cut a few 2" wide strips and it helps a lot getting the kayfun apart. Thanks.
Now they are a permanent addition to my coil kit.